Question

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

Answer 1

Answer:

$27^{\frac{1}{3}}=3$

Step-by-step 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,

$n^{\frac{a}{b}}=\sqrt[b]{n^{a}}\\27^{\frac{1}{3}}=\sqrt[3]{27}=\sqrt[3]{3*3*3}=3$

Answer 2

Answer:

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 ($3 \times 3 \times 3$)

27 can be rewritten as $3^{3}$

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

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

Hence we get,

$\left(3^{3}\right)^{\frac{1}{3}}=3^{\frac{3}{1} \times \frac{1}{3}}$

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

$\left(3^{3}\right)^{\frac{1}{3}}=3$

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