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Popular >

simplify 5^{1/3}*25^{3/2}

Solution

simplify

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

Solution

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

+1

Solution steps

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

Factor the number:

25 = 5^{2}

= 5^{\frac{1}{3}} (5^{2})^{\frac{3}{2}}

Apply exponent rule:

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

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

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

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

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

5^{3} = 125

= 5^{\frac{1}{3}} \cdot 125

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Frequently Asked Questions (FAQ)

What is 5^{1/3}*25^{3/2} ?
The solution to 5^{1/3}*25^{3/2} is 5^{1/3}*125