Question

Which of the following is equivalent to the expression below? Select all that apply $5x \frac{3}{2}$A) $\sqrt[3]{(5x) {}^{2} }$B$5 \sqrt{x ^{3} }$C$\sqrt{(5x) ^{3} }$D$5( \sqrt{x) ^{3} }$E$\sqrt{5x ^{3} }$

Answer 1

Answer:

5√(x³) and 5(√x)³

Explanation:

We will use the following properties:

$\begin{gathered} \sqrt[]{x^a}=x^{\frac{a}{2}} \\ \sqrt[]{x^a}=(\sqrt[]{x})^a \end{gathered}$

Now, the expression is equivalent to:

$5x^{\frac{3}{2}}=5\cdot x^{\frac{3}{2}}=5\cdot\sqrt[]{x^3}$

And it is also equal to:

$5\sqrt[]{x^3}=5(\sqrt[]{x}^{})^3$

Therefore, the equivalent expressions are 5√(x³) and 5(√x)³