Question

Which expression is equivalent to O x³ (3√√y) O + (3√√) *²7 (2√x) x24 (3√y) # (x²²y) 3³7 x27 Which expression is equivalent to O x³ ( 3√√y ) O + ( 3√√ ) * ²7 ( 2√x ) x24 ( 3√y ) # ( x²²y ) 3³7 x27

Answer 1

`=x^9(\sqrt[3]{y})`

Step-by-step explanation

When an exponent is a fraction, we can write it as a radical as follows:

`x^{(a)/(b)}=\sqrt[b]{x^a}`

Then, based on the latter, our expression can be rewritten as follows:

`(x^(27)y)^{(1)/(3)}=\sqrt[3]{(x^(27)y)^1}`
`(x^(27)y)^{(1)/(3)}=\sqrt[3]{x^(27)y}`

Now, we must simplify x, as it has an exponent of 27, meaning:

`=\sqrt[3]{x^(27)}\cdot\sqrt[3]{y}`
`=x^9\cdot\sqrt[3]{y}`