What is 31^{2/3}(-4)^{2/3} ?

The solution to 31^{2/3}(-4)^{2/3} is 124^{2/3}

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simplify 31^{2/3}(-4)^{2/3}

simplify

3 1^{\frac{2}{3}} (- 4)^{\frac{2}{3}}

12 4^{\frac{2}{3}}

Decimal Notation

24.86648 \dots

Solution steps

3 1^{\frac{2}{3}} (- 4)^{\frac{2}{3}}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

3 1^{\frac{2}{3}} (- 4)^{\frac{2}{3}} = (31 (- 4))^{\frac{2}{3}}

= (31 (- 4))^{\frac{2}{3}}

31 (- 4) = - 124

= (- 124)^{\frac{2}{3}}

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- 124)^{\frac{2}{3}} = (- 1)^{\frac{2}{3}} \cdot 12 4^{\frac{2}{3}}

= (- 1)^{\frac{2}{3}} \cdot 12 4^{\frac{2}{3}}

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

= 1 \cdot 12 4^{\frac{2}{3}}

Multiply:

1 \cdot 12 4^{\frac{2}{3}} = 12 4^{\frac{2}{3}}

= 12 4^{\frac{2}{3}}

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(sin^{2} (x))^{\frac{3}{2}}

(400 \cdot 1 0^{- 3}) (0.6 \cdot 1 0^{6})^{2}

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(7.72 \cdot 1 0^{- 2}) (3.17)