Question

Using Laws of exponents, simplify and write the answer in exponential form:
$\left(i\right)3^2\times 3^4\times 3^3$

$\left(ii\right)8^4÷8^2$

$\left(iii\right)(3^4{)}^3$

Answer 1

$\left(i\right)$

$\begin{array}{cc}{3}^2\times 3^3\times 3^4& =3^{2+3+4}\text{by using}{a}^m\times a^n=a^{m+n}\\ & =3^{5+4}\\ & =3^9\end{array}$

$\left(ii\right)$

$\begin{array}{cc}{8}^4÷8^2& =\frac{8^4}{8^2}\\ & =8^{4-2}\text{by using}\frac{a^m}{a^n}=a^{m-n}\\ & =8^2\\ & =64\end{array}$

$\left(iii\right)$

$\begin{array}{cc}{\left(3^4\right)}^3& =3^{3\times 4}\text{by using}(a^m{)}^n=a^{mn}\\ & =3^{12}\end{array}$