Answer:
The answer is
[tex]{3n}^{9} [/tex]
Step-by-step explanation:
Volume of a cube = l³
where
l is the length of one side
From the question the volume is [tex] {27n}^{27} [/tex]
The length of one side is
[tex] {l}^{3} = {27n}^{27} [/tex]
Find the cube root of both sides
That's
[tex]l = \sqrt[3]{ {27n}^{27} } [/tex]
Write the equation in exponent form
That's
[tex] \sqrt[3]{ {3}^{3} {n}^{27} } [/tex]
But
[tex] \sqrt[3]{x} = {x}^{ \frac{1}{3} } [/tex]
So we have
[tex]( { {3}^{3} {n}^{27} })^{ \frac{1}{3} } = {3}^{3 \times \frac{1}{3} } \times {n}^{27 \times \frac{1}{3} } [/tex]
We have
[tex]3 \times {n}^{9} [/tex]
So we have the final answer as
[tex] {3n}^{9} [/tex]
Hope this helps you
