Question

Simplify the expression. Write your answer as a power.

${\left(-9\right)}^4.{\left(-9\right)}^7$.

Answer 1

Given number: ${\left(-9\right)}^4.{\left(-9\right)}^7$.

We know that

${\left(\mathrm{a}\right)}^{\mathrm{m}}.{\left(\mathrm{a}\right)}^{\mathrm{n}}={\left(\mathrm{a}\right)}^{\mathrm{m}+\mathrm{n}}$

Now,

${\left(-9\right)}^4.{\left(-9\right)}^7={\left(-9\right)}^{4+7}$ $\left[\because {\left(\mathrm{a}\right)}^{\mathrm{m}}.{\left(\mathrm{a}\right)}^{\mathrm{n}}={\left(\mathrm{a}\right)}^{\mathrm{m}+\mathrm{n}}\right]$

$={\left(-9\right)}^{11}$

Hence, ${\left(-9\right)}^4.{\left(-9\right)}^7={\left(-9\right)}^{11}$.