Class 8 Exam  >  Class 8 Notes  >  Mathematics (Maths) Class 8  >  NCERT Solutions: Exponents & Powers(Exercise 10.1, 10.2)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Exercise 10.1

Q1: Evaluate

(i) 3-2
Sol: (i) To evaluate an expression of the form a-n,where a is a base and n is a positive exponent, we use the rule NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
This means we take the reciprocal of the base raised to the positive exponent. So, for 3-2 , this would be:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

(ii) (-4)-2
Sol: Applying the same rule to (-4)-2
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Note that the square of −4 is positive because squaring any real number (whether positive or negative) results in a non-negative number.

(iii) (1/2)-5
Sol: For this expression, we apply the same principle:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
In this case, 1/2 raised to the power of 5 gives 1/32 and taking the reciprocal of that gives us 32.
To summarize:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Q2: Simplify and express the result in power notation with positive exponent.
(i) (– 4)5 ÷ (– 4)8
Sol: When we divide powers with the same base, we subtract the exponents: 
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
(ii) (1/23)2

Sol: When we raise a power to another power, we multiply the exponents: 
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

(iii) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Sol: When multiplying powers with the same exponent but different bases, we can combine them under the same exponent:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

=−(1)×54 =−54
This result cannot be expressed with a positive exponent due to the negative sign in front of 54 .
(iv) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Sol: First, divide the powers with the same base:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Then, multiply by 3-5:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
To express with a positive exponent:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

(v) 2–3 × (–7)–3
Sol: Both bases are raised to negative exponents, so we find their reciprocals and multiply: 
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)


Q3: Find the value of 

(i) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
First, evaluate each term inside the parentheses:
30 =1 (Any number raised to the power of 0 is 1.)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)(Negative exponents indicate the reciprocal of the base raised to the positive exponent.)
So, the expression becomes:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
22 =4, thus:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

(ii)NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Simplify inside the parentheses first:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
For the division:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
So, the expression simplifies to:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
(iii) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Evaluate each term:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Summing them up:
4 + 9 + 16 = 29

(iv) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Any expression raised to the power of 0 is 1, regardless of what the expression inside the parentheses evaluates to. So, without needing to simplify the expression inside, the result is: 1

(v) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
First, evaluate the expression inside the curly braces:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
When raising a fraction to a negative exponent, you take the reciprocal of the base and then square it:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Then, raising this result to the power of 2:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Q4: Evaluate. 

(i) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Sol: First, simplify the numerator and the denominator separately:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
So, the expression becomes:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

(ii) NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Sol: Simplify each term:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
So, the expression becomes:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
To summarize:
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Q5: Find the value of m for which 

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Sol: To find the value of m for which NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1) we can use the properties of exponents to simplify the equation. When dividing numbers with the same base, you subtract the exponents:

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
So, we have:
5m+3 = 55
For this equation to be true, the exponents on both sides must be equal (since the bases are the same and non-zero). Therefore, we set the exponents equal to each other:
m + 3 = 5
To solve for m, we subtract 3 from both sides:
m=5−3
m=2
So, the value of m for which the original equation holds true is 2.
Q6: Evaluate. 

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Sol: (i)NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
= (3-4) = -1
(ii)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Q7: Simplify. 

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Sol: (i)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

   NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

(ii) 

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1) 

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

Exercise 10.2

Q1. Express the following numbers in standard form.
(i) 0.0000000000085
Sol:
This number is 8.5 followed by 11 decimal places to the left, so in standard form, it is:
8.5 × 1 0 − 12

(ii) 0.00000000000942
Sol:
This number is 9.42 followed by 11 decimal places to the left, so in standard form, it is:
9.42 × 1 0 − 12 

(iii) 6020000000000000
Sol:
This number is 6.02 followed by 15 places to the right, so in standard form, it is: 6.02 × 10 15

(iv) 0.00000000837
Sol: 
This number is 8.37 followed by 9 decimal places to the left, so in standard form, it is: 8.37 × 10 − 9

(v) 31860000000
Sol: 
This number is 3.186 followed by 10 places to the right, so in standard form, it is:
3.186 × 1 010 

Q2: Express the following numbers in usual form.
(i) 3.02×10−6
Sol:
 Shift the decimal point 6 places to the left:
0.00000302

(ii) 4.5 * 104
Sol:
Shift the decimal point 4 places to the right:
45,000

(iii) 3 * 10–8
Sol:
 Shift the decimal point 8 places to the left:
0.00000003

(iv) 1.0001 * 109
Sol:
Shift the decimal point 9 places to the right:
1,000,100,000

(v) 5.8 * 1012
Sol:
 Shift the decimal point 12 places to the right:
5,800,000,000,000

(vi) 3.61492 * 106
Sol:
Shift the decimal point 6 places to the right: 
3,614,920

Q3. Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)
Sol:
This can be written as:
1×10−6m

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
Sol:
This is:
1.6×10 −19 coulomb

(iii) Size of a bacteria is 0.0000005 m.
Sol:
 This can be expressed as:
5×10 −7 m

(iv) Size of a plant cell is 0.00001275 m.
Sol: 
This is:1.275×10 −5 m

(v) Thickness of a thick paper is 0.07 mm.
Sol: 
To express this in meters and in standard form (considering 1 mm = 0.001 m 1 mm=0.001 m):
0.07 mm=0.07×0.001 m=7×10 −2 m

Q4: In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
Sol: 
To find the total thickness of the stack, we need to sum the thicknesses of all the books and paper sheets.
Books Each book has a thickness of 20 mm. For 5 books, the total thickness is:
5 × 20 mm = 100 mm
Paper Sheets
Each paper sheet has a thickness of 0.016 mm. For 5 paper sheets, the total thickness is:
5×0.016mm=0.08mm
Total Thickness
Adding the thicknesses of the books and paper sheets together gives the total thickness of the stack:
100mm+0.08mm=100.08mm
Therefore, the total thickness of the stack is 100.08 mm.

The document NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1) is a part of the Class 8 Course Mathematics (Maths) Class 8.
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FAQs on NCERT Solutions for Class 8 Maths - Exponents and Powers - 1 (Exercise 10.1)

1. What is an exponent?
Ans. An exponent is a number that represents how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number.
2. How do you simplify expressions with exponents?
Ans. To simplify expressions with exponents, you can use the rules of exponents such as multiplying exponents with the same base, dividing exponents with the same base, and raising a power to a power.
3. What is the difference between a base and an exponent?
Ans. The base in an exponential expression is the number that is being multiplied by itself, while the exponent is the number that represents how many times the base is multiplied by itself.
4. How do you solve problems involving negative exponents?
Ans. To solve problems involving negative exponents, you can rewrite the expression with a positive exponent by moving the base to the denominator if the exponent is negative.
5. Can exponents be fractions or decimals?
Ans. Yes, exponents can be fractions or decimals. In such cases, the exponent represents the number of times the base is multiplied by itself, either in fractional parts or decimal parts.
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