Question

Which expression is equivalent to the following please show your work.

Answer 1

One of the properties of power is the power of a power property:

`(x^a)^b=x^(a\cdot b)`

Then, the given expression is:

`16x^(15)`

The power of a product property is:

`(a\cdot b)^x=a^x\cdot b^x`

If we apply it to the option D we obtain:

`\begin{gathered} (4x^6)^2\cdot x^3=4^2\cdot(x^6)^2\cdot x^3 \\ \text{Now} \\ 4^2=4\cdot4=16 \\ \text{And} \\ (x^6)^2=x^(6\cdot2)=x^(12) \\ \text{Then we have:} \\ (4x^6)^2\cdot x^3=16x^(12)\cdot x^3 \end{gathered}`

Finally, let's apply the product of powers property:

`x^a\cdot x^b=x^(a+b)`

Then, we obtain:

`(4x^6)^2\cdot x^3=16x^(12+3)=16x^(15)`

The answer is option D.