Question

Simplify and express each of the following in exponential form: $\frac{3^7}{(3^4\times 3^3)}$.

Answer 1

Simplify the expression $\frac{3^7}{(3^4\times 3^3)}$

$=\frac{3^7}{\left(3^{4+3}\right)}$ $\mathbf{}\mathbf{[}\mathbf{\because }{\mathbf{a}}^{\mathbf{m}}\mathbf{\times }\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\mathbf{]}$

$=\frac{3^7}{3^7}$

$=3^{7-7}$ $\mathbf{[}\mathbf{\because }{\mathbf{a}}^{\mathbf{m}}\mathbf{÷}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{-}\mathbf{n}}\mathbf{]}$

$=3^0$

$=1$

Therefore, $\frac{3^7}{(3^4\times 3^3)}$$=1$.