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All questions of Exponents and Powers for Class 7 Exam

The value of (4- 20) x 5is
  • a)
    1
  • b)
    0
  • c)
    10
  • d)
    -10
Correct answer is option 'B'. Can you explain this answer?

Sreemoyee Nair answered
Anything raised to the power zero is 1 .
In the given expression,  (4- 20) x 50
                                             = (1 - 1) x 1
                                      = ( 0 ) x 1
                                      = 0
So Option B is correct answer. 

The value of (−1)500 is
  • a)
    1
  • b)
    -1
  • c)
    0
  • d)
    None of these

Correct answer is option 'A'. Can you explain this answer?

If any power having a even number is raised to -1 then the  result will be 1
Since the power is an even number , So (−1)500 =  1 

The value of (−1)47 is
  • a)
    -1
  • b)
    1
  • c)
    0
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Nitin Patel answered
If any power having a odd number is raised to -1 then result will be -1
So (−1)47 = -1
So option A is correct answer. 

In 2the exponent is
  • a)
    1
  • b)
    5
  • c)
    2
  • d)
    0
Correct answer is option 'B'. Can you explain this answer?

Shalini Menon answered
Exponents, or powers, are a way of indicating that a quantity is to be multiplied by itself some number of times. In the expression 252 is called the base and 5 is called the exponent, or power.

The value of (−1)400 is
  • a)
    1
  • b)
    0
  • c)
    -1
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Krish Sen answered
If any power having an even number is raised to -1 then the  result will be 1
Since the power is an even number , So (−1)400 =  1 
So option A is the correct answer. 

Express 2048 as a power 2.
  • a)
    28
  • b)
    211
  • c)
    210
  • d)
    29
Correct answer is option 'B'. Can you explain this answer?

Abhiram Chavan answered
 2048 = 2 x 1024
= 2 x 2 x 512
= 2 x 2 x 2 x 256
= 2 x 2 x 2 x 2x 128
= 2 x 2 x 2 x 2 x 2 x 64
= 2 x 2 x 2 x 2 x 2 x 2 x 32
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 16
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 8
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 211
So option B is the correct answer. 

The value of (−1)55 is
  • a)
    1
  • b)
    -1
  • c)
    0
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

If any power having a odd number is raised to -1 then result will be -1
So (−1)55 = -1
So option B is correct answer. 

The multiplicative inverse of 7-2 is:
  • a)
    7
  • b)
    7
  • c)
    1/72
  • d)
    1/7
Correct answer is option 'A'. Can you explain this answer?

Shounak Desai answered
Understanding the Problem
The question asks for the multiplicative inverse of the expression \(7 - 2\). To find the multiplicative inverse, we first need to simplify the expression.
Step 1: Simplify the Expression
- Calculate \(7 - 2\):
- \(7 - 2 = 5\)
Now, we have the simplified expression as 5.
Step 2: Find the Multiplicative Inverse
- The multiplicative inverse of a number \(x\) is defined as \(\frac{1}{x}\).
- For the number 5, the multiplicative inverse is:
- \(\frac{1}{5}\)
Analyzing the Options
The options provided are:
- a) 72
- b) 7
- c) \(\frac{1}{72}\)
- d) \(\frac{1}{7}\)
None of these options represent the multiplicative inverse of 5, which is \(\frac{1}{5}\).
Correct Answer Evaluation
It seems there is a misunderstanding regarding the correct answer being option 'A' (72). The multiplicative inverse of 5 is not any of the choices listed, including 72.
Conclusion
To clarify:
- The multiplicative inverse of \(7 - 2\) (which equals 5) is \(\frac{1}{5}\).
- The correct answer should be based on the definition of the multiplicative inverse, which does not match any of the provided options.
Thus, the analysis shows the correct answer is not option 'A', but rather \(\frac{1}{5}\), which is not listed among the options.

(2/7)2 x (2/7)4 is equal to:
  • a)
    (4/7)8
  • b)
    (2/7)2
  • c)
    ( 2/7)6
  • d)
    (4/14)6
Correct answer is option 'C'. Can you explain this answer?

Gopal Kumar answered
Whenever you multiply two terms with the same base, you can add the exponents:
( x m ) ( x n ) = x( m + n )
So 
(2/7)2 x (2/7)4  = (2/7)6
So option C is the correct answer. 

Mark the correct answer:
3² × 10³ × 30 is less than 8.1 × 10⁵
  • a)
    True
  • b)
    False
  • c)
    Can’t say anything
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Understanding the Expression
To determine whether 3² × 10³ × 30 is less than 8.1 × 10, we first need to calculate the left side of the equation.
Step 1: Calculate 3²
- 3² = 9
Step 2: Calculate 10³
- 10³ = 1000
Step 3: Calculate 3² × 10³
- 9 × 1000 = 9000
Step 4: Multiply by 30
- 9000 × 30 = 270000
Step 5: Evaluate 8.1 × 10
- 8.1 × 10 = 81
Comparison of Values
Now we compare the two results:
- Left Side: 270000
- Right Side: 81
Since 270000 is significantly greater than 81, we conclude that:
Final Conclusion
- 3² × 10³ × 30 is NOT less than 8.1 × 10.
Thus, the statement "3² × 10³ × 30 is less than 8.1 × 10" is False, leading us to the correct answer being option 'b'.
However, if the correct answer was stated as 'A', it could be an error.
Always double-check calculations!
Final Answer
- The correct answer should actually be option 'B' (False).

Express 27 in exponential form.
  • a)
  • b)
  • c)
    3⁴
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Megha bhatia answered
Understanding Exponential Form
Exponential form is a way to express numbers using a base and an exponent. The exponent indicates how many times the base is multiplied by itself.
Finding the Exponential Form of 27
To express 27 in exponential form, we need to identify a base and an exponent that, when combined, equal 27.
Breaking Down the Number 27
- Recognize that 27 is a product of smaller numbers.
- Start with the prime factorization of 27.
- 27 can be expressed as:
27 = 3 × 3 × 3
Expressing as Exponents
- Since we have three 3s multiplied together, we can represent this using exponents.
- This gives us:
27 = 3^3
Evaluating the Options
Now, let's evaluate the provided options:
- a) 3^2 = 9 (not equal to 27)
- b) 3^3 = 27 (this is correct)
- c) 3 (not equal to 27)
- d) None of these (this is incorrect)
Conclusion
The correct exponential form of 27 is 3^3, confirming that option 'B' is indeed the right answer. Understanding this process helps strengthen your number sense and factorization skills, which are essential in mathematics.

(20 + 30) × 40 =
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

Vp Classes answered
(20 + 30) × 40 =
To solve the expression, we apply the rule that any number raised to the power of zero equals 1. Therefore:
  • 20 = 1
  • 30 = 1
  • 40 = 1
Now, substituting these values into the expression:
(1 + 1) × 1 = 2
Thus, the final answer is 2.

Express 10,000,000 in the exponential form.

  • a)
    10⁵

  • b)
    10⁶

  • c)
    10⁷

  • d)
    10⁸

Correct answer is option 'C'. Can you explain this answer?
?

Subham Iyer answered
Understanding Exponential Form
Exponential form is a way to express large numbers using powers of 10. For example, the number 10,000,000 can be represented as 10 raised to a power.
Breaking Down 10,000,000
- The number 10,000,000 has a total of 7 zeros after the 1.
- To express this in exponential form, we need to count the number of times we multiply 10 by itself.
Finding the Exponent
- 10,000,000 can be rewritten as 10 x 10 x 10 x 10 x 10 x 10 x 10.
- This is the same as 10 raised to the power of 7 because we are multiplying 10 by itself 7 times.
Final Expression
- Thus, 10,000,000 in exponential form is written as 10^7.
- Therefore, the correct option is 10^7, which corresponds to option 'C'.
Conclusion
- In summary, when converting large numbers to exponential form, count the zeros to determine the exponent.
- For 10,000,000, the final expression is 10^7.
Understanding this concept helps in simplifying and working with large numbers more efficiently!

Mark the greatest number of all:
3.1 × 10³, 3 × 10², and 1.1 × 10⁵
  • a)
    3.1 × 10³
  • b)
    3 × 10²
  • c)
    1.1 × 10⁵
  • d)
    Can’t say anything
Correct answer is option 'C'. Can you explain this answer?

Since we have:
3.1 × 10³, 3 × 10², and 1.1 × 10⁵
3.1 × 10³ = 3.1 × 1000 = 3100
3 × 10² = 3 × 100 = 300
1.1 × 10⁵ = 1.1 × 100000 = 110000
Clearly, 110000 is the greatest number of all.
Hence, C is the correct answer.

The value of 
  • a)
    26×316×512
  • b)
    317×516×75
  • c)
    26×516×712
  • d)
    27×317×75
Correct answer is option 'B'. Can you explain this answer?

Correct Answer :- b
Explanation :  [(2*3)12 * (5*7)28 * (5*3)16]/[(7*2)12 * (7*3)11 * 528]
= [(2)12 * (3)12 * (5)28 * (7)28 * (5)16 * (3)16]/[(7)12 * (2)12 * (7)11 * (3)11 * (5)28]
= [(2)12 * (3)12+16 * (5)28+16 * 316]/[(7)12+11 * (2)12 * (3)11 * (5)28]
= [(2)12 * (3)28 * (5)44 * 316]/[(7)23 * (2)12 * (3)11 * (5)28]
= 317 * 516 * 75

If  a = 3 and b = 4 then find the value of aa + bb
  • a)
    283
  • b)
    270
  • c)
    276
  • d)
    267
Correct answer is option 'A'. Can you explain this answer?

Gopal Kumar answered
Given, a = 3 and b = 4 
aa + b= 33 + 4= 3 x 3 x 3 + 4 x 4 x 4 x 4
                            = 27 + 16 x 16 
                            = 27 + 256
                            = 283
So option A is the correct answer. 
 

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