Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 29 Answers Solutions Chapter 6 Indices.

## Indices Class 7 Practice Set 29 Answers Solutions Chapter 6

Question 1.
Simplify:
i. $$\left[\left(\frac{15}{12}\right)^{3}\right]^{4}$$
ii. (34)-2
iii. $$\left[\left(\frac{1}{7}\right)^{-3}\right]^{4}$$
iv. $$\left[\left(\frac{2}{5}\right)^{-2}\right]^{-3}$$
v. (65)4
vi. $$\left[\left(\frac{6}{7}\right)^{5}\right]^{2}$$
vii. $$\left[\left(\frac{2}{3}\right)^{-4}\right]^{5}$$
viii. $$\left[\left(\frac{5}{8}\right)^{3}\right]^{-2}$$
ix. $$\left[\left(\frac{3}{4}\right)^{6}\right]^{7}$$
x. $$\left[\left(\frac{2}{5}\right)^{-3}\right]^{2}$$
Solution:
i. $$\left[\left(\frac{15}{12}\right)^{3}\right]^{4}$$
$$=\left(\frac{15}{12}\right)^{3 \times 4}=\left(\frac{15}{12}\right)^{12}$$

ii. (34)-2
= 34×(-2)
= 3-8

iii. $$\left[\left(\frac{1}{7}\right)^{-3}\right]^{4}$$
$$=\left(\frac{1}{7}\right)^{(-3) \times 4}=\left(\frac{1}{7}\right)^{-12}$$

iv. $$\left[\left(\frac{2}{5}\right)^{-2}\right]^{-3}$$
$$=\left(\frac{2}{5}\right)^{(-2) \times(-3)}=\left(\frac{2}{5}\right)^{6}$$

v. (65)4
= 65×4
= 620

vi. $$\left[\left(\frac{6}{7}\right)^{5}\right]^{2}$$
$$=\left(\frac{6}{7}\right)^{5 \times 2}=\left(\frac{6}{7}\right)^{10}$$

vii. $$\left[\left(\frac{2}{3}\right)^{-4}\right]^{5}$$
$$=\left(\frac{2}{3}\right)^{(-4) \times 5}=\left(\frac{2}{3}\right)^{-20}$$

viii. $$\left[\left(\frac{5}{8}\right)^{3}\right]^{-2}$$
$$=\left(\frac{5}{8}\right)^{3 \times(-2)}=\left(\frac{5}{8}\right)^{-6}$$

ix. $$\left[\left(\frac{3}{4}\right)^{6}\right]^{7}$$
$$=\left(\frac{3}{4}\right)^{6 \times 1}=\left(\frac{3}{4}\right)^{6}$$

x. $$\left[\left(\frac{2}{5}\right)^{-3}\right]^{2}$$
$$=\left(\frac{2}{5}\right)^{(-3) \times 2}=\left(\frac{2}{5}\right)^{-6}$$

Question 2.
Write the following numbers using positive indices:
i. $$\left(\frac{2}{7}\right)^{-2}$$
ii. $$\left(\frac{11}{3}\right)^{-5}$$
iii. $$\left(\frac{1}{6}\right)^{-3}$$
iv. $$(y)^{-4}$$
Solution:
i. $$\left(\frac{7}{2}\right)^{2}$$
ii. $$\left(\frac{3}{11}\right)^{5}$$
iii. $$6^{3}$$
iv. $$\frac{1}{y^{4}}$$