Question

Simplify and express the answer in the positive exponenet form:
(i) $\frac{(-3{)}^3\times 2^6}{6\times 2^3}$
(ii) $\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}$

Answer 1

(i) $\frac{(-3{)}^3\times 2^6}{6\times 2^3}$
It can be written as
$\frac{(-3{)}^3\times 2^6}{2\times 3\times 2^3}$
On further calculation
$\frac{(-3{)}^3\times 2^6}{3\times 2^{3+1}}$
So we get
$=-(3{)}^{3-1}{2}^{6-4}$
$=-(3{)}^2{2}^2$
$=-3^2{2}^2$

(ii) $\frac{(2^3{)}^5\times 5^4}{4^3\times 5^2}$
It can be written as
$=\frac{2^{3\times 5}\times 5^4}{2^3\times 2^2\times 5^2}$
On further calculation
$=\frac{2^{15}\times 5^4}{2^6\times 5^2}$
So we get
$=2^{15-6}\times 5^{4-2}$
$=2^9\times 5^2$