## Maharashtra State Board Class 7 Maths Solutions Chapter 6 Indices Practice Set 28

Question 1.

Simplify:

i. a^{6} ÷ a^{4}

ii. m^{5} ÷ m^{8}

iii. p^{3} ÷ p^{13}

iv. x^{10} ÷ x^{10}

Solution:

i. a^{6} ÷ a^{4}

= a^{6-4}

= a^{2}

ii. m^{5} ÷ m^{8}

= m^{5-8}

= m^{-3}

iii. p^{3} ÷ p^{13}

= p^{3-13}

= p^{-10}

iv. x^{10} ÷ x^{10}

= x^{10-10}

= x^{0}^{
}= 1

Question 2.

Find the value of:

i. (-7)^{12} ÷ (-7)^{12}

ii. 7^{5} ÷ 7^{3}

iii. \(\left(\frac{4}{5}\right)^{3} \div\left(\frac{4}{5}\right)^{2}\)

iv. 4^{7} ÷ 4^{5}

Solution:

i. (-7)^{12} ÷ (-7)^{12}

= (-7)^{12-12}

= (-7)^{0}

= 1

ii. 7^{5} ÷ 7^{3}

= 7^{5-3}

= 7^{2}

= 49

iii. \(\left(\frac{4}{5}\right)^{3} \div\left(\frac{4}{5}\right)^{2}\)

\(=\left(\frac{4}{5}\right)^{3-2}=\frac{4}{5}\)

iv. 4 ÷ 4

= 4^{7-5}

= 4^{2}

= 16