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Important Questions for Class 8 Maths - Exponents and Powers

Q1: Evaluate
(i) 2^-2
(ii) (-2)^-2
(iii) (3/2)^-5

Sol:
As we know that
b^-n= 1/bⁿ
(i) 2^-2 = 1/ 2² =1/4
(ii) (-2)^-2 = 1/(-2)²= 1/4
(iii) (3/2)^-5 = 3^-5/ 2^-5 =2⁵/3⁵ = 32/243

Q2: Find the value of.
(i) (4⁰ + 4^-1) × 2²
(ii) (3^-1 × 9^-1) ÷ 3^-2
(iii)(11^-1 + 12^-1 + 13^-1)⁰

Sol:
(i) (4⁰ + 4^-1) × 2² = (1+1/4) × 4 = 4 + 1 =5
(ii) (3^-1 × 9^-1) ÷ 3^-2 = [(1/3) × (1/9)] ÷ (1/9) =1/3
(iii) (11^-1 + 12^-1 + 13^-1)⁰=1 as a⁰= 1

Q3: Find the value of m for which 2^m ÷ 2^-4 = 4⁵

Sol:
2^m ÷ 2^-4 = 4⁵
2^m × (1/2^-4) = 2¹⁰
2^m+4 =2¹⁰
So m + 4 = 10
m = 6

Q4: Express the following numbers in usual form.
(i) 34.02 x 10^-5
(ii) 9.5 x 10⁵
(iii) 9 x 10^-4
(iv) 2.0001 x 10⁸

Sol:
(i) 34.02 x 10^-5 = .0003402
(ii) 9.5 x 10⁵= 950000
(iii) 9 x 10^-4= .0009
(iv) 2.0001 x 10⁸=200010000

Q5: Find the Multiplicative inverse of
(i) $3^{25}$
(ii) $4^{- 3}$
(iii) $(\frac{2}{3})^{- 2}$

$(\frac{2}{3})^{- 2}$
(i) The multiplicative inverse of a number is the number that, when multiplied by the original number, equals 1.
To find the multiplicative inverse of 3^25, we need to find the number that, when multiplied by 3^25, equals 1.
The multiplicative inverse of 3²⁵ is (3²⁵)^(-1) = 1/(3²⁵).

$(\frac{2}{3})^{- 2}$

$(\frac{2}{3})^{- 2}$
(i) Very small numbers can be expressed in standard form using negative exponents.
(ii) $a^{p} \times b^{q} = (a b)^{p q}$
(iii) $.00567 = 5.67 \times 10^{- 3}$
(iv) $\frac{1}{(8)^{- 3}} = 2^{9}$
(v) $4^{0} = 4$
(vi) $(- 1)^{3} = 1$
(vii) The multiplicative inverse of $(- 2)^{- 2}$ is $(2)^{2}$ .

Ans:
(i) True
(ii) False
(iii) True
(iv) True as $\frac{1}{(8)^{- 3}} = 8^{3} = (2^{3})^{3} = 2^{9}$
(v) False
(vi) False
(vii) True as $(- 2)^{- 2} = \frac{1}{4}$

$(- 2)^{- 2} = \frac{1}{4}$
Ans:
(p) → (ii)
(q) → (iii)
(r) → (iv)
(s) → (i)

Q8: The multiplicative inverse of $(- 7)^{- 2} \div (90)^{- 1}$ is
(a) $- (7)^{2} \times (90)^{- 1}$
(b) $- (7)^{-} 2 \times (90)^{- 1}$
(c) $- (7)^{2} \div (90)^{- 1}$
(d) $- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$ $- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$
$- (7)^{2} \times (90)^{1}$

$- (7)^{2} \times (90)^{1}$

Sol:

Q13: Express the following numbers in standard form.
(i) 0.0000000015
(ii) 0.00000001425
(iii) 102000000000000000

Sol:
(i) 0.0000000015 = 1.5 ×10^-9
(ii) 0.00000001425 = 1.425×10^-8
(iii) 102000000000000000 = 1.02×10¹⁷

Q14: Solve for the variables

Sol:

Q15: Simplify the following

Sol:

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FAQs on Important Questions for Class 8 Maths - Exponents and Powers

1. What is an exponent?

Ans. An exponent represents the number of 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 an expression with exponents?

Ans. To simplify an expression with exponents, you need to apply the rules of exponents. For example, if you have a product of two numbers with the same base raised to different exponents, you can add the exponents together.

3. What is the difference between a power and an exponent?

Ans. An exponent is the number of times a base number is multiplied by itself, while a power is the result of raising a base number to an exponent. In other words, the exponent tells you how many times to multiply the base number to get the power.

4. How do negative exponents work?

Ans. Negative exponents indicate the reciprocal of a number. For example, if you have a number raised to the power of -2, it means you take the reciprocal of that number and square it. So, x^-2 is equal to 1/x^2.

5. Can you simplify expressions with exponents using the order of operations?

Ans. Yes, you can simplify expressions with exponents using the order of operations. It is important to perform any operations inside parentheses first, then evaluate exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

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