Answer:
A. [tex]9m^{3}[/tex]
Step-by-step explanation:
We have been given an exponential expression [tex](81m^6)^{\frac{1}{2}[/tex]. We are asked to choose the option that is equivalent to our given expression.
Using exponent property [tex](ab)^n=a^n\cdot b^n[/tex], we will get:
[tex](81m^6)^{\frac{1}{2}}=81^{\frac{1}{2}}\cdot (m^6)^{\frac{1}{2}}[/tex]
We can write 81 as [tex]9^2[/tex].
[tex](81m^6)^{\frac{1}{2}}=(9^2)^{\frac{1}{2}}\cdot m^{6\times\frac{1}{2}}[/tex]
Using exponent property [tex](a^m)^n=a^{m\cdot n}[/tex], we will get:
[tex](81m^6)^{\frac{1}{2}}=9^{2\times\frac{1}{2}}\cdot m^{6\times\frac{1}{2}}[/tex]
[tex](81m^6)^{\frac{1}{2}}=9^{1}\cdot m^{3}[/tex]
[tex](81m^6)^{\frac{1}{2}}=9m^{3}[/tex]
Therefore, [tex]9m^{3}[/tex] is equivalent to our given expression and option A is the correct choice.
