Question

What is the simplified value of the exponential expression 27 Superscript one-third?

Answer 1

The simplified value of the exponential expression 27 superscript one-third is 3.

Solution:

Given that the number is 27 superscript one-third.

Since three power three gives 27 (
`3 * 3 * 3`)

27 can be rewritten as
`3^(3)`

Now 27 superscript one third is written as
`\left(3^(3)\right)^{(1)/(3)}`

Apply the power rule and multiply exponents,
`\left(\mathrm{a}^{\mathrm{m}}\right)^{\mathrm{n}=\mathrm{a}^{\mathrm{mn}}}`

Hence we get,

`\left(3^(3)\right)^{(1)/(3)}=3^{(3)/(1) * (1)/(3)}`

The powers 3 in the numerator and denominator cancel each other. Thus we get the solution as 3.

`\left(3^(3)\right)^{(1)/(3)}=3`

Hence the simplified value of the exponential expression 27 superscript one-third is 3.

Answer 2

`27^{(1)/(3)}=3`

Explanation:

According to the Exponents Law. When We have a number raised to a fraction as having the root of one number, whose index is the denominator of one number raised to the numerator.

So,

`n^{(a)/(b)}=\sqrt[b]{n^(a)}\\27^{(1)/(3)}=\sqrt[3]{27}=\sqrt[3]{3*3*3}=3`