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prealgebra intermediate

Problem

If

x \geq 0

, then

x x x =

(A)

x x

(B)

x 4 x

(C)

8 x

(D)

8 x^{3}

(E)

8 x^{7}

Solution

Recall that square roots are one-half powers, namely

y = y^{\frac{1}{2}}

for all

y \geq 0.

We have

x x x = x x \cdot x^{\frac{1}{2}} = x x^{\frac{3}{2}} = x \cdot (x^{\frac{3}{2}})^{\frac{1}{2}} = x^{\frac{7}{4}} = (x^{\frac{7}{4}})^{\frac{1}{2}} = x^{\frac{7}{8}} = 8 x^{7} .

Final answer

E