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Popular >

simplify 128^{1/3}

Solution

simplify

12 8^{\frac{1}{3}}

Solution

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

+1

Solution steps

12 8^{\frac{1}{3}}

Prime factorization of

128 : 2^{7}

= (2^{7})^{\frac{1}{3}}

Apply exponent rule:

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

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

= (2^{6} \cdot 2)^{\frac{1}{3}}

Apply exponent rule:

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

(2^{6} \cdot 2)^{\frac{1}{3}} = (2^{6})^{\frac{1}{3}} \cdot 2^{\frac{1}{3}}

= (2^{6})^{\frac{1}{3}} \cdot 2^{\frac{1}{3}}

(2^{6})^{\frac{1}{3}} = 4

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

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Frequently Asked Questions (FAQ)

What is 128^{1/3} ?
The solution to 128^{1/3} is 4*2^{1/3}