Question

Which expression is equivalent to 64x6y4z3 ?A)16x2y43 zB)4x2y43 zC)4x3yD)643x2y43 z

Answer 1

We have the following mathematical expression:

`\sqrt[3]{64x^6y^4z^3}`

From which we must find an equivalent expression, To solve this, we must remember a rule of exponents.

`\sqrt[m]{a^n}=a^{(n)/(m)}`

with the above rule we will divide all the exponents of the terms inside the root over 3 and also solve the 64 cubic raiz which is:

`\sqrt[3]{64}=4`

Now we simplify the mathematical expression:

`\begin{gathered} \sqrt[3]{64x^6y^4z^3} \\ \sqrt[3]{64\cdot}\sqrt[3]{x^6}\cdot\sqrt[3]{y^4^{}}\cdot\sqrt[]{z^3} \\ 4\cdot x^{(6)/(3)}\cdot y^{(4)/(3)}\cdot z^{(3)/(3)} \\ 4x^2\cdot y^{(4)/(3)}\cdot z \end{gathered}`

In conclusion, the answer is:

`4x^2y^{(4)/(3)}z`