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Popular >

simplify (5y^{1/2})^4

Solution

simplify

(5 y^{\frac{1}{2}})^{4}

Solution

625 y^{2}

Solution steps

(5 y^{\frac{1}{2}})^{4}

Apply exponent rule:

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

(5 y^{\frac{1}{2}})^{4} = 5^{4} (y^{\frac{1}{2}})^{4}

= 5^{4} (y^{\frac{1}{2}})^{4}

5^{4} = 625

= 625 (y^{\frac{1}{2}})^{4}

Apply exponent rule:

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

assuming

a \geq 0

(y^{\frac{1}{2}})^{4} = y^{\frac{1}{2} \cdot 4}

= 625 y^{\frac{1}{2} \cdot 4}

\frac{1}{2} \cdot 4 = 2

= 625 y^{2}

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Frequently Asked Questions (FAQ)

What is (5y^{1/2})^4 ?
The solution to (5y^{1/2})^4 is 625y^2