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Popular >

simplify (100v^{2/5})^{3/2}

Solution

simplify

(100 v^{\frac{2}{5}})^{\frac{3}{2}}

Solution

1000 v^{\frac{3}{5}}

Solution steps

(100 v^{\frac{2}{5}})^{\frac{3}{2}}

Apply exponent rule:

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

(100 v^{\frac{2}{5}})^{\frac{3}{2}} = 10 0^{\frac{3}{2}} (v^{\frac{2}{5}})^{\frac{3}{2}}

= 10 0^{\frac{3}{2}} (v^{\frac{2}{5}})^{\frac{3}{2}}

10 0^{\frac{3}{2}} = 1000

= 1000 (v^{\frac{2}{5}})^{\frac{3}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

= 1000 v^{\frac{2}{5} \cdot \frac{3}{2}}

Cross-cancel:

2

= 1000 v^{\frac{3}{5}}

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Frequently Asked Questions (FAQ)

What is (100v^{2/5})^{3/2} ?
The solution to (100v^{2/5})^{3/2} is 1000v^{3/5}