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Popular >

simplify 125^{3/2}

Solution

simplify

12 5^{\frac{3}{2}}

Solution

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

+1

Decimal Notation

1397.54248 \dots

Solution steps

12 5^{\frac{3}{2}}

Prime factorization of

125 : 5^{3}

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Apply exponent rule:

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

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

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

(5^{2})^{\frac{3}{2}} = 125

= 125 \cdot 5^{\frac{3}{2}}

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

= 125 \cdot 5 \cdot 5^{\frac{1}{2}}

Multiply the numbers:

125 \cdot 5 = 625

= 625 \cdot 5^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is 125^{3/2} ?
The solution to 125^{3/2} is 625*5^{1/2}