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Popular >

simplify (125^{2/3})^{1/2}

Solution

simplify

(12 5^{\frac{2}{3}})^{\frac{1}{2}}

Solution

5

Solution steps

(12 5^{\frac{2}{3}})^{\frac{1}{2}}

Apply exponent rule:

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

= 12 5^{\frac{2}{3} \cdot \frac{1}{2}}

Cross-cancel:

2

= 12 5^{\frac{1}{3}}

Factor the number:

125 = 5^{3}

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

Apply exponent rule:

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

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

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

= 5^{1}

Apply exponent rule:

a^{1} = a

= 5

Popular Examples

factor 6x^3+12x^2y-x-2y factor

6 x^{3} + 12 x^{2} y - x - 2 y

2 x^{2} - 12 x = 0

simplify 3/10+1/4 simplify

\frac{3}{10} + \frac{1}{4}

3 (3 v - 4) = 51

simplify 3+1/6 simplify

3 + \frac{1}{6}

Frequently Asked Questions (FAQ)

What is (125^{2/3})^{1/2} ?
The solution to (125^{2/3})^{1/2} is 5