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Popular >

simplify 2/3 (25)^{3/2}

Solution

simplify

\frac{2}{3} (25)^{\frac{3}{2}}

Solution

\frac{250}{3}

+1

Decimal Notation

83.33333 \dots

Solution steps

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

Factor the number:

25 = 5^{2}

= \frac{2}{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}}

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

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

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

5^{3} = 125

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

\frac{2}{3} \cdot 125 = \frac{250}{3}

= \frac{250}{3}

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Frequently Asked Questions (FAQ)

What is 2/3 (25)^{3/2} ?
The solution to 2/3 (25)^{3/2} is 250/3