Question

Simplify and express each of the following in exponential form:$({\left(5^2\right)}^3\times 5^4)÷5^7$

Answer 1

Simplification of expression: $({\left(5^2\right)}^3\times 5^4)÷5^7$

${\left(5^2\right)}^3$can be expressed as ${\left(5\right)}^{2\times 3}$ $\mathbf{[}\mathbf{\because }{\mathbf{\left(}{\mathbf{a}}^{\mathbf{m}}\mathbf{\right)}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{mn}}\mathbf{]}$

$=5^6$

Then,

$=(5^6\times 5^4)÷5^7$

$=\left(5^{6+4}\right)÷5^7$ $\mathbf{[}\mathbf{\because }{\mathbf{a}}^{\mathbf{m}}\mathbf{\times }{\mathbf{a}}^{\mathbf{n}}\mathbf{=}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\mathbf{]}$

$=5^{10}÷5^7$

$=5^{10-7}$ $\mathbf{[}\mathbf{\because }{\mathbf{a}}^{\mathbf{m}}\mathbf{÷}{\mathbf{a}}^{\mathbf{n}}\mathbf{=}{\mathbf{a}}^{\mathbf{m}\mathbf{-}\mathbf{n}}\mathbf{]}$

$=5^3$

Therefore, $({\left(5^2\right)}^3\times 5^4)÷5^7$$=5^3$.