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Popular >

simplify (sqrt(5x^2y^3))^8

Solution

simplify

(5 x^{2} y^{3})^{8}

Solution

625 x^{8} y^{12}

Solution steps

(5 x^{2} y^{3})^{8}

Rewrite

8

as

2 \cdot 4

= (5 x^{2} y^{3})^{2 \cdot 4}

Apply exponent rule:

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

assuming

a \geq 0

(5 x^{2} y^{3})^{2 \cdot 4} = ((5 x^{2} y^{3})^{2})^{4}

= ((5 x^{2} y^{3})^{2})^{4}

Apply exponent rule:

assuming

n i s o dd or a \geq 0

(5 x^{2} y^{3})^{2} = 5 x^{2} y^{3}

= (5 x^{2} y^{3})^{4}

Apply exponent rule:

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

(5 x^{2} y^{3})^{4} = 5^{4} (x^{2})^{4} (y^{3})^{4}

= 5^{4} (x^{2})^{4} (y^{3})^{4}

5^{4} = 625

= 625 (x^{2})^{4} (y^{3})^{4}

Simplify

(x^{2})^{4} : x^{8}

= 625 x^{8} (y^{3})^{4}

Simplify

(y^{3})^{4} : y^{12}

= 625 x^{8} y^{12}

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Frequently Asked Questions (FAQ)

What is (sqrt(5x^2y^3))^8 ?
The solution to (sqrt(5x^2y^3))^8 is 625x^8y^{12}