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Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Important Questions: Exponents and Powers

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.

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

$(\frac{2}{3})^{- 2}$
(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
(v) False
(vi) False
(vii) True as $(- 2)^{- 2} = \frac{1}{4}$

$(- 2)^{- 2} = \frac{1}{4}$

Ans:therefore correct match is :
(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 are exponents and how are they used in mathematical expressions?

Ans.Exponents are a way to represent repeated multiplication of a number by itself. For example, in the expression $2^3$, the number 2 is the base, and 3 is the exponent, which means $2 \times 2 \times 2 = 8$. Exponents simplify calculations involving large numbers and are widely used in various mathematical applications.

2. How do you multiply numbers with exponents?

Ans.To multiply numbers with the same base, you add their exponents. For example, $a^m \times a^n = a^{m+n}$. If the bases are different, you cannot combine them directly using exponents and must multiply them as regular numbers.

3. What is the rule for dividing numbers with exponents?

Ans.When dividing numbers with the same base, you subtract their exponents. The rule is $a^m \div a^n = a^{m-n}$. This is applicable as long as the base $a$ is not equal to zero.

4. How do you evaluate a power of zero, such as $a^0$?

Ans.Any non-zero number raised to the power of zero equals 1. So, $a^0 = 1$ for any $a \neq 0$. This is an important rule in exponentiation that helps in simplifying expressions.

5. What are some real-life applications of exponents and powers?

Ans.Exponents and powers are used in various real-life applications, such as calculating areas and volumes, understanding scientific notation for very large or small numbers, and in fields like computer science for algorithm complexity. They also appear in finance when calculating compound interest, and in physics when dealing with large quantities like the speed of light.

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