Question

Write an expression that simplifies to ${\mathrm{x}}^{24}$ using the Power of a Power Property.

Answer 1

To simplify ${\mathrm{x}}^{24}$ using the Power of a Power Property, we use general rule for finding ${\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}$ power of a power,
If two powers have the same base then we can multiply the powers as ${\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}\times \mathrm{n}}$ ,

Here$\mathrm{m}\times \mathrm{n}=24$, lets take $\mathrm{m},\mathrm{n}$ as $12,2$

So that$12\times 2=24$,

Therefore ${\left({\mathrm{x}}^{12}\right)}^2={\mathrm{x}}^{12\times 2}={\mathrm{x}}^{24}$.
Hence, the expression is ${\mathrm{x}}^{24}={\left({\mathrm{x}}^{12}\right)}^2$ .