Free Printable Index roots and power laws

Worksheets

Name

Class

Date

Convert the following into the form of

a^{\frac{m}{n}}

\left(^3\sqrt{4}\right)^2

$4^6$

$4^{\frac{3}{2}}$

$4^{\frac{2}{3}}$

Change the following into the form of

\left(a^m\right)^{\frac{1}{n}}

5^{\frac{k}{3}}

$\left(5^k\right)^{\frac{1}{3}}$

$\left(5^3\right)^{\frac{1}{k}}$

$\left(5^k\right)^3$

Convert the following into the form of

^n\sqrt{a^m}

x^{\frac{6}{7}}

$^x\sqrt{6^7}$

$^6\sqrt{x^7}$

$^7\sqrt{x^6}$

Convert the following into the form of

\left(^n\sqrt{a}\right)^m

7^{\frac{i}{2}}

$\left(^i\sqrt{7}\right)^2$

$\left(\sqrt{7}\right)^i$

$\left(^3\sqrt{7}\right)^i$

$k^{\frac{r}{3}}=\left(k^3\right)^{\frac{1}{r}}$
Does the statement above true or false? Choose the correct answer with suitable reason.

True. Both sides are equal.

False. The right-hand side is $\left(k^r\right)^{\frac{1}{3}}$

False. The right-hand side is $\left(k^r\right)^3$

100 %

Similar Resources on Wayground