HBSE 8th Class Maths Solutions Chapter 12 Exponents and Powers Ex 12.1

Haryana State Board HBSE 8th Class Maths Solutions Chapter 12 Exponents and Powers Ex 12.1 Textbook Exercise Questions and Answers.

Haryana Board 8th Class Maths Solutions Chapter 12 Exponents and Powers Exercise 12.1

Question 1.
Evaluate :
(i) 3^-2
(ii) (-4)^-2
(iii) \(\left(\frac{1}{2}\right)^{-5}\)
Solution:

Question 2.
Simplify and express the result in power notation with positive exponent.
(i) (-4)⁵, (-4)⁶
(ii) \(\left(\frac{1}{2^{3}}\right)^{2}\)
(iii) (-3)⁴ × \(\left(\frac{5}{3}\right)^{4}\)
(iv) (3^-7 ÷ 3^-10) × 3^-5
(v) 2^-5 × (-7)^-3.
Solution:
(i) ∵ a^m ÷ aⁿ = a^m-n
∴ (-4)⁵ ÷ (-4)⁸ = (-4)^5-8

= +1 × 5⁴ = 5⁴
= 5 × 5 × 5 × 5
= 625.

(iv) ∵ a^m ÷ aⁿ = a^m-n
and a^m × aⁿ = a^m+n
∴ (3^-7 ÷ 3^-10) × 3^-5 = 3^-7-(-10) × 3^-5
= 3^-7+10 × 3^-5
= 3³ × 3^-5

Question 3.
Find the value of :
(i) (3⁰ + 4^-1) × 2²
(ii) (2^-1 × 4^-1), 2^-2
(iii) \(\left(\frac{1}{2}\right)^{-2}\) + \(\left(\frac{1}{3}\right)^{-2}\) + \(\left(\frac{1}{4}\right)^{-2}\)
(iv) (3^-1 + 4^-1 + 5^-1)⁰
(v) \(\left\{\left(\frac{-2}{3}\right)^{-2}\right\}^{2}\)
Solution:

Question 4.
Evaluate:
(i) \(\frac{8^{-1} \times 5^{3}}{2^{-4}}\)
(ii) (5^-1 × 2^-1) × 6^-1
Solution:

Question 5.
Find the value of m for which 5^m ÷ 5^-3 = 5⁵
Solution:
∵ a^m ÷ a^m = a^m-n
∴ 5^m ÷ 5^-3 = 5⁵
or 5^m-(-3) = 5⁵
or 5^m+3 = 5⁵ [∵ a^m = aⁿ]
or m + 3 = 5 [∵ m = n]
or m = 5 – 3
∴ m = 2

Question 6.
Evaluate:
(i) \(\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}\)
(ii) \(\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4}\)
Solution:

Question 7.
Simplify:
(i) \(\frac{25 \times t^{-4}}{5^{-3} \times 10 \times t^{-8}}\) (t ≠ 0)
(ii) \(\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}\)
Solution:


= 5^10-5 = 5⁵
= 5 × 5 × 5 × 5 × 5
= 3125.