Question

Which of the following is equivalent to 5 square root 13^3

A.13^2
B.13^15
C.12^5/3
D.13^3/5

Answer 1

For this case we must find an expression equivalent to the following:

`5 \sqrt {13 ^ 3}`

By definition of properties of powers and roots we have:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

In addition, we know that:

`13 ^ 3 = 13 ^ 2 * 13`

Rewriting the given expression we have:

`5 \sqrt {13 ^ 3} = 5 \sqrt {13 ^ 2 * 13} = 13 * 5 \sqrt {13} = 65 \sqrt {13}`

Answer:

`65 \sqrt {13}`