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Which of the following is equivalent to the expression below? Select all that apply
5x (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) }

Which of the following is equivalent to the expression below? Select all that apply-example-1
User Kiran Kumar
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1 Answer

23 votes
23 votes

Answer:

5√(x³) and 5(√x)³

Step-by-step explanation:

We will use the following properties:


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

Now, the expression is equivalent to:


5x^{(3)/(2)}=5\cdot x^{(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

User Rubenvb
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3.6k points