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Popular >

simplify 32^{1/3}

Solution

simplify

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

Solution

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

+1

Decimal Notation

3.17480 \dots

Solution steps

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

Prime factorization of

32 : 2^{5}

= (2^{5})^{\frac{1}{3}}

Apply exponent rule:

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

2^{5} = 2^{3} \cdot 2^{2}

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

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

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

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

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Frequently Asked Questions (FAQ)

What is 32^{1/3} ?
The solution to 32^{1/3} is 2*2^{2/3}