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

Which of the following is equivalent to the expression below Select all that apply tex5x frac32 texA tex sqrt35x 2 texBtex5 sqrtx 3 texCtex sqrt5x 3 texDtex5 sq class=

Respuesta :

Answer:

5√(x³) and 5(√x)³

Explanation:

We will use the following properties:

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

Now, the expression is equivalent to:

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

And it is also equal to:

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

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

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