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) ∵ am ÷ an = am-n
∴ (-4)5 ÷ (-4)8 = (-4)5-8
= +1 × 54 = 54
= 5 × 5 × 5 × 5
= 625.
(iv) ∵ am ÷ an = am-n
and am × an = am+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 5m ÷ 5-3 = 55
Solution:
∵ am ÷ am = am-n
∴ 5m ÷ 5-3 = 55
or 5m-(-3) = 55
or 5m+3 = 55 [∵ am = 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:
= 510-5 = 55
= 5 × 5 × 5 × 5 × 5
= 3125.