MATH SOLVE

4 months ago

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

Accepted Solution

A:

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 ([tex]3 \times 3 \times 3[/tex])27 can be rewritten as [tex]3^{3}[/tex]Now 27 superscript one third is written as [tex]\left(3^{3}\right)^{\frac{1}{3}}[/tex]Apply the power rule and multiply exponents, [tex]\left(\mathrm{a}^{\mathrm{m}}\right)^{\mathrm{n}=\mathrm{a}^{\mathrm{mn}}}[/tex]Hence we get,[tex]\left(3^{3}\right)^{\frac{1}{3}}=3^{\frac{3}{1} \times \frac{1}{3}}[/tex]
The powers 3 in the numerator and denominator cancel each other. Thus we get the solution as 3.
[tex]\left(3^{3}\right)^{\frac{1}{3}}=3[/tex]Hence the simplified value of the exponential expression 27 superscript one-third is 3.