Class 8 Maths Exponents and Power Worksheet Set A - Free Printable

Final Answer:
1. $ 4^{-1} - 8^{-1} = \frac{1}{8} $, and $ \left(\frac{2}{3}\right)^{-1} = \frac{3}{2} $, so $ \frac{1}{8} \div \frac{3}{2} = \frac{1}{12} $

2a. $ \left(-\frac{8}{13}\right)^{-1} + \left(\frac{16}{5}\right)^{-1} - \left(-\frac{4}{5}\right)^{-1} = -\frac{13}{8} + \frac{5}{16} + \frac{5}{4} = -\frac{1}{16} $

2b. $ \left[\left(-\frac{2}{3}\right)^{-1}\right]^{-1} = -\frac{2}{3} $

3. Multiplicative inverse of $ 15^4 $ is $ 15^{-4} $

4. $ 5^0 \times 3^{-1} = 1 \times \frac{1}{3} = \frac{1}{3} $

5a. $ (-4)^3 \times (-4)^{-8} = (-4)^{-5} $

5b. $ 2^6 \times 2^9 = 2^{15} $

5c. $ \left(\frac{2}{3}\right)^{-4} \div \left(\frac{2}{3}\right)^7 \times \left(\frac{2}{3}\right)^{11} = \left(\frac{2}{3}\right)^0 = 1 $

5d. $ (-2)^3 \times (-2)^{-3} = (-2)^0 = 1 $

6a. $ \frac{4^{-3} \times a^{-2} \times b^{-4}}{4^{-5} \times a^{-4} \times b^3} = 4^{2} \times a^{2} \times b^{-7} = \frac{16a^2}{b^7} $

6b. $ \frac{10^{-4} \times 9^{-4}}{2^{-4} \times 15^{-4}} = \left(\frac{10 \times 9}{2 \times 15}\right)^{-4} = 3^{-4} = \frac{1}{81} $

7a. $ 4^{3x-1} = 16^{2x-5} \Rightarrow 4^{3x-1} = (4^2)^{2x-5} = 4^{4x-10} \Rightarrow 3x - 1 = 4x - 10 \Rightarrow x = 9 $

7b. $ 2^{2x+3} = 1 \Rightarrow 2x + 3 = 0 \Rightarrow x = -\frac{3}{2} $

8a. $ \left(-\frac{2}{5}\right)^{-2} + \left(-\frac{2}{5}\right)^{-1} = \frac{25}{4} - \frac{5}{2} = \frac{15}{4} $, so $ \frac{15}{4} = \frac{4m}{25} \Rightarrow m = \frac{375}{16} $

8b. $ (25)^{-4} = 5^m \Rightarrow (5^2)^{-4} = 5^{-8} = 5^m \Rightarrow m = -8 $

9a. $ 836000000 = 8.36 \times 10^8 $

9b. $ 0.000000045 = 4.5 \times 10^{-8} $

9c. $ 0.00000306 = 3.06 \times 10^{-6} $

9d. $ \frac{6102}{10000} = 0.6102 = 6.102 \times 10^{-1} $

10a. $ 6.34 \times 10^{-5} = 0.0000634 $

10b. $ 8.9 \times 10^4 = 89000 $

10c. $ 6 \times 10^{-3} = 0.006 $

10d. $ 2.3456 \times 10^3 = 2345.6 $