Question

Simplify and express the answer in the positive exponent form:​
(i) $\frac{(-3{)}^3\times 2^6}{6\times 2^3}$

Answer 1

Given, $\frac{(-3{)}^3\times 2^6}{6\times 2^3}$

It can be written as:

$\frac{(-3{)}^3\times 2^6}{6\times 2^3}=\frac{(-3{)}^3\times 2^6}{2\times 3\times 2^3}$

On further calculation , we have :

$\frac{(-3{)}^3\times 2^6}{6\times 2^3}=\frac{(-3{)}^3\times 2^6}{3\times 2^{3+1}}$
[$\because$ $a^m\times a^n=a^{m+n}$]

$=(-1{)}^3(3{)}^{3-1}\times 2^{6-4}$

$=-(3{)}^2\times 2^2$

Hence, $\frac{(-3{)}^3\times 2^6}{6\times 2^3}=-(3{)}^2\times 2^2$.