What is expand {5(2x^2z^4)^3(x^3y^3)^2}^2 ?

The solution to expand {5(2x^2z^4)^3(x^3y^3)^2}^2 is 1600x^{24}z^{24}y^{12}

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expand {5(2x^2z^4)^3(x^3y^3)^2}^2

expand

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

1600 x^{24} z^{24} y^{12}

Solution steps

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

Simplify

5 (2 x^{2} z^{4})^{3} (x^{3} y^{3})^{2} : 2^{3} \cdot 5 x^{12} z^{12} y^{6}

= (2^{3} \cdot 5 x^{12} z^{12} y^{6})^{2}

Apply exponent rule:

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

= 5^{2} (2^{3})^{2} (y^{6})^{2} (z^{12})^{2} (x^{12})^{2}

(2^{3})^{2} : 2^{6}

= 5^{2} \cdot 2^{6} (z^{12})^{2} (x^{12})^{2} (y^{6})^{2}

(z^{12})^{2} : z^{24}

= 5^{2} \cdot 2^{6} z^{24} (x^{12})^{2} (y^{6})^{2}

(x^{12})^{2} : x^{24}

= 5^{2} \cdot 2^{6} z^{24} x^{24} (y^{6})^{2}

(y^{6})^{2} : y^{12}

= 5^{2} \cdot 2^{6} z^{24} x^{24} y^{12}

Refine

= 1600 x^{24} z^{24} y^{12}

\frac{( a + a \cdot b ) ^{2}}{c ( a - b )}

- a \cdot (ln (b \cdot N) + 1)

2 (x + y) d x - x (x + 2 y - 2) d y

(2 - m) ln (3 x + 100)

\frac{2 ( x ^{2} - 2 ln ( x ^{2} + 1 ) ( x ^{2} + 1 ) )}{3 x ^{5} ( x ^{2} + 1 )}

What is expand {5(2x^2z^4)^3(x^3y^3)^2}^2 ?
The solution to expand {5(2x^2z^4)^3(x^3y^3)^2}^2 is 1600x^{24}z^{24}y^{12}