Question

Using laws of exponents , simplify and write the answer in exponential form:

$\left(2^{12}÷2^7\right)\times 9^{-5}$

Answer 1

Given,

$$\begin{gathered} \left(2^{12}÷2^7\right)\times 9^{-5} \\ =2^{12}\times 2^{-7}\times 9^{-5} \\ =2^{12-7}\times 9^{-5} \\ =2^5\times 9^{-5} \\ =2^5÷9^5 \\ ={\left(\frac{2}{9}\right)}^5 \end{gathered}$$ [ Using exponent law : $a^{-n}=\frac{1}{a^n}$ and $a^n\times a^m=a^{m+n}$ ]

Hence, required value is ${\left(\frac{2}{9}\right)}^5$ .