## Maharashtra State Board Class 7 Maths Solutions Chapter 6 Indices Practice Set 27

Question 1.

Simplify:

i. 7^{4} × 7^{2}

ii. (-11)^{5} × (-11)^{2}

iii. \(\left(\frac{6}{7}\right)^{3} \times\left(\frac{6}{7}\right)^{5}\)

iv. \(\left(-\frac{3}{2}\right)^{5} \times\left(-\frac{3}{2}\right)^{3}\)

v. a^{16} × a^{7}

vi. \(\left(\frac{\mathrm{P}}{5}\right)^{3} \times\left(\frac{\mathrm{P}}{5}\right)^{7}\)

Solution:

i. 7^{4} × 7^{2}

= 7^{4+2}

= 7^{6}

ii. (-11)^{5} × (-11)^{2}

= (-11)^{5+2}

= (-11)^{7}

iii. \(\left(\frac{6}{7}\right)^{3} \times\left(\frac{6}{7}\right)^{5}\)

\(=\left(\frac{6}{7}\right)^{3+5}=\left(\frac{6}{7}\right)^{8}\)

iv. \(\left(-\frac{3}{2}\right)^{5} \times\left(-\frac{3}{2}\right)^{3}\)

\(=\left(-\frac{3}{2}\right)^{5+3}=\left(-\frac{3}{2}\right)^{8}\)

v. a^{16} × a^{7}

= a^{16+7}

= a^{23}

vi. \(\left(\frac{\mathrm{P}}{5}\right)^{3} \times\left(\frac{\mathrm{P}}{5}\right)^{7}\)

\(=\left(\frac{\mathrm{P}}{5}\right)^{3+7}=\left(\frac{\mathrm{P}}{5}\right)^{10}\)