What is 1000(0.5)^{80/30} ?

The solution to 1000(0.5)^{80/30} is 2^{1/3}*125

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simplify 1000(0.5)^{80/30}

simplify

1000 (0.5)^{\frac{80}{30}}

2^{\frac{1}{3}} \cdot 125

Decimal Notation

157.49013 \dots

Solution steps

1000 \cdot 0. 5^{\frac{80}{30}}

0.5 = \frac{1}{2}

= 1000 (\frac{1}{2})^{\frac{80}{30}}

Cancel the common factor:

10

= 1000 (\frac{1}{2})^{\frac{8}{3}}

Apply exponent rule:

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

(\frac{1}{2})^{\frac{8}{3}} = \frac{1 ^{\frac{8}{3}}}{2 ^{\frac{8}{3}}}

= 1000 \cdot \frac{1 ^{\frac{8}{3}}}{2 ^{\frac{8}{3}}}

\frac{1 ^{\frac{8}{3}}}{2 ^{\frac{8}{3}}} = \frac{1}{4 \cdot 2 ^{\frac{2}{3}}}

= 1000 \cdot \frac{1}{4 \cdot 2 ^{\frac{2}{3}}}

1000 \cdot \frac{1}{4 \cdot 2 ^{\frac{2}{3}}} = 2^{\frac{1}{3}} \cdot 125

= 2^{\frac{1}{3}} \cdot 125

16 n^{3} + 32 n^{2} - n - 2

3 (- 2) + 2

(x + 4) (x - 9) \geq 0

\frac{7}{8} + \frac{9}{20}

(- 36)^{\frac{1}{2}}