What is (8x^3)^{1/3} ?

The solution to (8x^3)^{1/3} is 2x

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simplify (8x^3)^{1/3}

simplify

(8 x^{3})^{\frac{1}{3}}

2 x

Solution steps

(8 x^{3})^{\frac{1}{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(8 x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}} (x^{3})^{\frac{1}{3}}

= 8^{\frac{1}{3}} (x^{3})^{\frac{1}{3}}

8^{\frac{1}{3}} = 2

= 2 (x^{3})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(x^{3})^{\frac{1}{3}} = x^{3 \cdot \frac{1}{3}}

= 2 x^{3 \cdot \frac{1}{3}}

3 \cdot \frac{1}{3} = 1

= 2 x^{1}

Apply exponent rule:

a^{1} = a

x^{1} = x

= 2 x

\frac{( x - y ) ^{5}}{( y - x ) ^{5}}

\frac{( \frac{( x ^{2} + 3 )}{4} ) ^{2} - ( x ^{3} + x )}{2}

- \frac{7}{8} \cdot a^{2} \cdot b^{5} \cdot \frac{c ^{8}}{( - \frac{5}{2} )} \cdot a \cdot b^{5} \cdot c^{6}

8 y + y

2 \frac{a}{b ^{- 1}} + 5 \frac{b}{a ^{- 1}}