Answer :
To find the cube root of [tex]\(8x^{27}\)[/tex], we can break it down into two parts: finding the cube root of the numerical coefficient (8) and finding the cube root of the variable expression ([tex]\(x^{27}\)[/tex]).
1. Cube Root of 8:
[tex]\[
\text{The cube root of } 8 = 2
\][/tex]
Since [tex]\(2^3 = 8\)[/tex], the cube root of 8 is 2.
2. Cube Root of [tex]\(x^{27}\)[/tex]:
[tex]\[
\text{The cube root of } x^{27} = x^{27/3} = x^9
\][/tex]
We divide the exponent 27 by 3 because we are finding the cube root.
Now, putting it all together, the cube root of [tex]\(8x^{27}\)[/tex] is:
[tex]\[
2 \cdot x^9 = 2x^9
\][/tex]
So, the answer is [tex]\(2x^9\)[/tex].
1. Cube Root of 8:
[tex]\[
\text{The cube root of } 8 = 2
\][/tex]
Since [tex]\(2^3 = 8\)[/tex], the cube root of 8 is 2.
2. Cube Root of [tex]\(x^{27}\)[/tex]:
[tex]\[
\text{The cube root of } x^{27} = x^{27/3} = x^9
\][/tex]
We divide the exponent 27 by 3 because we are finding the cube root.
Now, putting it all together, the cube root of [tex]\(8x^{27}\)[/tex] is:
[tex]\[
2 \cdot x^9 = 2x^9
\][/tex]
So, the answer is [tex]\(2x^9\)[/tex].
