Question

Explain why $\sqrt{x^4}=x^2$ Then explain why$\sqrt{x^{16}}=x^8$.

Short answer

We have proved that$\sqrt{x^4}=x^2\mathrm{and}\sqrt{x^{16}}=x^8$.

Step-by-step solution

Step 1. Given information.

The given statement is:

Explain why$\sqrt{x^4}=x^2\mathrm{and}\sqrt{x^{16}}=x^8$.

Step 2. Explain that x4=x2.

As we know that $\left(a^m\right)=a^{m·n}$.

Therefore, we can say that:

${\left(x^2\right)}^2=x^4$,

and$\sqrt{x^4}=x^2$

Step 3. Explain that x16=x8.

Since ${\left(x^8\right)}^2=x^{16}$

then$\sqrt{x^{16}}=x^8$