Question

Which is equivalent

Answer 1

Answer:

A. $9m^{3}$

Step-by-step explanation:

We have been given an exponential expression $(81m^6)^{\frac{1}{2}$. We are asked to choose the option that is equivalent to our given expression.

Using exponent property $(ab)^n=a^n\cdot b^n$, we will get:

$(81m^6)^{\frac{1}{2}}=81^{\frac{1}{2}}\cdot (m^6)^{\frac{1}{2}}$

We can write 81 as $9^2$.

$(81m^6)^{\frac{1}{2}}=(9^2)^{\frac{1}{2}}\cdot m^{6\times\frac{1}{2}}$

Using exponent property $(a^m)^n=a^{m\cdot n}$, we will get:

$(81m^6)^{\frac{1}{2}}=9^{2\times\frac{1}{2}}\cdot m^{6\times\frac{1}{2}}$

$(81m^6)^{\frac{1}{2}}=9^{1}\cdot m^{3}$

$(81m^6)^{\frac{1}{2}}=9m^{3}$

Therefore, $9m^{3}$ is equivalent to our given expression and option A is the correct choice.

Answer 2

Answer:

A. 9m³

Step-by-step explanation: