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.
Answer:
[tex]27^{\frac{1}{3}}=3[/tex]
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,
[tex]n^{\frac{a}{b}}=\sqrt[b]{n^{a}}\\27^{\frac{1}{3}}=\sqrt[3]{27}=\sqrt[3]{3*3*3}=3[/tex]
