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Popular >

simplify (750/512)^{1/3}

Solution

simplify

(\frac{750}{512})^{\frac{1}{3}}

Solution

\frac{5 \cdot 3 ^{\frac{1}{3}}}{4 \cdot 2 ^{\frac{2}{3}}}

+1

Decimal Notation

1.13570 \dots

Solution steps

(\frac{750}{512})^{\frac{1}{3}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{75 0 ^{\frac{1}{3}}}{51 2 ^{\frac{1}{3}}}

75 0^{\frac{1}{3}} = 5 \cdot 6^{\frac{1}{3}}

= \frac{5 \cdot 6 ^{\frac{1}{3}}}{51 2 ^{\frac{1}{3}}}

51 2^{\frac{1}{3}} = 8

= \frac{5 \cdot 6 ^{\frac{1}{3}}}{8}

Factor

6^{\frac{1}{3}} : 2^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

Factor

8 : 2^{3}

= \frac{5 \cdot 2 ^{\frac{1}{3}} \cdot 3 ^{\frac{1}{3}}}{2 ^{3}}

Cancel

\frac{5 \cdot 2 ^{\frac{1}{3}} \cdot 3 ^{\frac{1}{3}}}{2 ^{3}} : \frac{5 \cdot 3 ^{\frac{1}{3}}}{2 ^{\frac{8}{3}}}

= \frac{5 \cdot 3 ^{\frac{1}{3}}}{2 ^{\frac{8}{3}}}

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

= \frac{5 \cdot 3 ^{\frac{1}{3}}}{2 ^{2} \cdot 2 ^{\frac{2}{3}}}

2^{2} = 4

= \frac{5 \cdot 3 ^{\frac{1}{3}}}{4 \cdot 2 ^{\frac{2}{3}}}

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Frequently Asked Questions (FAQ)

What is (750/512)^{1/3} ?
The solution to (750/512)^{1/3} is (5*3^{1/3})/(4*2^{2/3)}