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Popular >

simplify 32^{2/3}

Solution

simplify

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

Solution

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

+1

Decimal Notation

10.07936 \dots

Solution steps

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

Prime factorization of

32 : 2^{5}

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

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

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

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

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

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

Multiply the numbers:

4 \cdot 2 = 8

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

Popular Examples

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\frac{186000000 π}{8765.8 \cdot 4}

x^{2} - 4 x - 224 = 0

- \frac{1}{2} x - 7 = 18

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n^{2} - 30 n + 56

simplify-3(3/2)^0 simplify

- 3 (\frac{3}{2})^{0}

Frequently Asked Questions (FAQ)

What is 32^{2/3} ?
The solution to 32^{2/3} is 8*2^{1/3}