Write as a radical power

1. 3√13^2

2. √(2/3)^5

2 answers

√ means the 1/2 power.

As with any exponents, powers of powers multiply exponents.

√(3^5) = (3^5)^(1/2) = 3^(5/2)
(√3)^5 = (3^(1/2))^5 = 3^(5/2)

Now try your problems.
1.

√ 13 ^ 2 = 13

3 √ 13 ^ 2 = 3 * 13 = 39

2.

( 2 / 3 ) ^ 5 = ( 2 / 3 ) ^ 4 * ( 2 / 3 ) =

[ ( 2 / 3 ) ^ 2 ] ^ 2 * ( 2 / 3 )

√ ( 2 / 3 ) ^ 5 = √ [ ( 2 / 3 ) ^ 2 ) ^ 2 ] * √ ( 2 / 3 ) =

( 2 / 3 ) ^ 2 * √ ( 2 / 3 ) =

( 4 / 9 ) * √ ( 2 / 3 ) =

4 * √ ( 2 / 3 ) / 9 =

4 * √ 2 / 9 * √ 3