What is 128^{2/3}*4^{2/3} ?

The solution to 128^{2/3}*4^{2/3} is 16*2^{2/3}*4^{2/3}

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simplify 128^{2/3}*4^{2/3}

simplify

12 8^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

16 \cdot 2^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

Decimal Notation

64

Solution steps

12 8^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

Prime factorization of

128 : 2^{7}

= (2^{7})^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{7} = 2^{6} \cdot 2

= (2^{6} \cdot 2)^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

Apply exponent rule:

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

(2^{6} \cdot 2)^{\frac{2}{3}} = (2^{6})^{\frac{2}{3}} \cdot 2^{\frac{2}{3}}

= (2^{6})^{\frac{2}{3}} \cdot 2^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

(2^{6})^{\frac{2}{3}} = 16

= 16 \cdot 2^{\frac{2}{3}} \cdot 4^{\frac{2}{3}}

e^{- 0.25}

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What is 128^{2/3}*4^{2/3} ?
The solution to 128^{2/3}*4^{2/3} is 16*2^{2/3}*4^{2/3}