Question

Law of radicals

Answer 1

Answer:

1)  $\sqrt{x^7}=x^{\frac{7}{2}$

2)  $\sqrt[3]{y^5}=y^{\frac{5}{3}$

3) $\sqrt[5]{a^{12}}=a^{\frac{12}{5} }$

4) $\sqrt[4]{z^{9}}=z^\frac{9}{4}$

Step-by-step explanation:

1) $\sqrt{x^7}$

We know that $\sqrt{x}=x^{\frac{1}{2}$

So, $\sqrt{x^7}=x^{\frac{7}{2}$

2) $\sqrt[3]{y^5}$

We know that $\sqrt[3]{x}=x^{\frac{1}{3}$

So, $\sqrt[3]{y^5}=y^{\frac{5}{3}$

3) $\sqrt[5]{a^{12}}$

We know that $\sqrt[5]{x}=x^{\frac{1}{5}$

So, $\sqrt[5]{a^{12}}=a^{\frac{12}{5} }$

4) $\sqrt[4]{z^{9}}$

We know that $\sqrt[4]{x}=x^{\frac{1}{4}$

So, $\sqrt[4]{z^{9}}=z^\frac{9}{4}$