Question

What is the simplified form of the square root r to the forty-ninth power?

Answer 1

Do you mean:
\[\sqrt{r}^{49}\]

Answer 2

\[\sqrt{r ^{49}}\]

Answer 3

you can write this as
\[ \sqrt{r^{48}} \sqrt{r} \]

Answer 4

\[\sqrt{x} = x^{\frac{1}{2}}\]

Answer 5

and remember that
\[ \sqrt{r^{48} } =\sqrt{ r^{24} r^{24} } \]

Answer 6

I think the simplified form would be the variable to a fractional exponent.

Answer 7

now "pull out" a pair from outside the square root.

Answer 8

\(\bf r^{49} \implies (r^{24})^2 \times r\)

Answer 9

\(\bf \sqrt{r^{49}} \implies \sqrt{(r^{24})^2 \times r}\)

Answer 10

it's to the 49th power, though.

Answer 11

\(\sqrt{x^5} = (x^5)^\frac{1}{2}\)
When raising a power to a power, the exponents are multiplied.
\(\sqrt{x^5} = (x^5)^\frac{1}{2}=x^\frac{5}{2}\)

Answer 12

the answer they are probably looking for is
\[r^{24} \sqrt{r} \]

Answer 13

thank you all! :)