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Popular Algebra >

simplify 512^{4/6}

Solution

simplify

51 2^{\frac{4}{6}}

Solution

64

Solution steps

51 2^{\frac{4}{6}}

Prime factorization of

512 : 2^{9}

= (2^{9})^{\frac{4}{6}}

Apply exponent rule:

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

2^{9} = 2^{6} \cdot 2^{3}

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

Apply exponent rule:

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

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

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

(2^{6})^{\frac{4}{6}} = 16

= 16 (2^{3})^{\frac{4}{6}}

Apply exponent rule:

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

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

= 16 \cdot 2^{3 \cdot \frac{4}{6}}

3 \cdot \frac{4}{6} = 2

= 16 \cdot 2^{2}

2^{2} = 4

= 16 \cdot 4

Multiply the numbers:

16 \cdot 4 = 64

= 64

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s im pl i f y \frac{\frac{1}{2 x}}{\frac{1}{2 y}}

Frequently Asked Questions (FAQ)

What is 512^{4/6} ?
The solution to 512^{4/6} is 64

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