Question

Simplify the expression.

the quantity x to the one fifteenth power end quantity to the power of 5

Answer 1

`\sqrt[3]{x}`.

Explanation:

We have been given an expression
`(x^{(1)/(15)})^5`. We are asked to simplify our given expression.

We will use power rule of exponents
`(a^b)^c=a^(b\cdot c)` to simplify our given expression as:

`(x^{(1)/(15)})^5=x^{(1)/(15)* 5}`

`(x^{(1)/(15)})^5=x^{(1)/(3)* 1}`

`(x^{(1)/(15)})^5=x^{(1)/(3)}`

Using fractional exponent rule
`a^{(1)/(n)}=\sqrt[n]{a}`, we can write our expression as:

`(x^{(1)/(15)})^5=\sqrt[3]{x}`

Therefore, the simplified form of our given expression would be
`\sqrt[3]{x}`.

Answer 2

`\sqrt[3]{x}`

Explanation:

we have

`(x^{(1)/(15)})^(5)`

Simplify

Multiply the exponents

`(x^{(1)/(15)})^(5)=x^{(1)/(15)*5}=x^{(5)/(15)}=x^{(1)/(3)}=\sqrt[3]{x}`