Question

What is the simplest form of the quotient? ^4sqrt810/^4sqrt2
1)^4sqrt162
2)3^4sqrt5
3)5^4sqrt3
4)3sqrt5

Answer 1

can you write it down

Answer 2

i have written down???

Answer 3

\[
\frac{\sqrt[4]{810}}{\sqrt[4]{2}}
\]Step one: use \(\color{blue}a^c / \color{red}b^c = (\color{blue}a /\color{red}b)^c\)\[
\frac{\sqrt[4]{\color{blue}{810}}}{\sqrt[4]{\color{red}2}} = \sqrt[4]{\frac{\color{blue}{810}}{\color{red}2}}
\]Step two: \[
\sqrt[4]{\frac{810}{2}}=\sqrt[4]{405}
\]Step three: We need to factor. Can you factor?

Answer 4

Facotr what? ^4sqrt405?

Answer 5

Factor 405 into prime numbers.

Answer 6

would it be factored by 5?

Answer 7

yeah that is one factor... keep going.

Answer 8

10?

Answer 9

\[
405 = 81 \times 5= 27\times 3\times 5=9\times 3\times 3\times 5=3\times 3\times 3\times 3\times 5 = 3^4\times 5
\]So

Answer 10

So that means \[
\sqrt[4]{405} =\sqrt[4]{ 3^4\times 5} = 3\sqrt[4]{5}
\]