What is (5x^2*y^2*m^3*n)^4 ?

The solution to (5x^2*y^2*m^3*n)^4 is 625x^8y^8m^{12}n^4

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simplify (5x^2y^2m^3*n)^4

simplify

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

625 x^{8} y^{8} m^{12} n^{4}

Solution steps

(5 x^{2} y^{2} m^{3} n)^{4}

Apply exponent rule:

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

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

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

5^{4} = 625

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

Simplify

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

= 625 x^{8} (y^{2})^{4} (m^{3})^{4} n^{4}

Simplify

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

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

Simplify

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

= 625 x^{8} y^{8} m^{12} n^{4}

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What is (5x^2*y^2*m^3*n)^4 ?
The solution to (5x^2*y^2*m^3*n)^4 is 625x^8y^8m^{12}n^4