Answer:
1,215 Superscript one-fifth x
Step-by-step explanation:
Given:
The expression to simplify is given as:
[tex](\sqrt[5]{1215})^x[/tex]
We know that,
[tex]\sqrt[n]{a} = a^{\frac{1}{n}}[/tex]
Here, [tex]n=5, a=1215[/tex]
So, [tex]\sqrt[5]{1215} = 1215^{\frac{1}{5}}[/tex]
So, the above expression becomes:
[tex](\sqrt[5]{1215})^x = (1215^{\frac{1}{5}})^x[/tex]
Now, using the law of indices [tex](a^m)^n=a^{(m\times n)}[/tex]
Here, [tex]a=1215,m=\frac{1}{5},n=x[/tex]
So, the expression is finally simplified to;
[tex]=(1215)^{({\frac{1}{5}}\times x)}\\\\=(1215)^{\frac{1}{5}x}[/tex]
Therefore, the second option is the correct one.
[tex](\sqrt[5]{1215})^x[/tex] = 1,215 Superscript one-fifth x
