Maharashtra Board Practice Set 29 Class 7 Maths Solutions Chapter 6 Indices

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. \(\frac{1}{y^{4}}\)

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