simplify ((x^3y^5z^5)^6)/((x^5y^5z)^5)

The original denominator must be nonzero:

{(x^{5} y^{5} z)}^{5}

≠ 0

Let's reduce:

\frac{{(x^{3} y^{5} z^{5})}^{6}}{{(x^{5} y^{5} z)}^{5}}

ⓘ The power of a product is the product of the powers:

{(x^{3} y^{5} z^{5})}^{6}

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

{(x^{5} y^{5} z)}^{5}

{(x^{5})}^{5} \cdot {(y^{5})}^{5} \cdot z^{5}

\frac{{(x^{3})}^{6} \cdot {(y^{5})}^{6} \cdot {(z^{5})}^{6}}{{(x^{5})}^{5} \cdot {(y^{5})}^{5} \cdot z^{5}}

We simplify the fraction:

\frac{{(y^{5})}^{6}}{{(y^{5})}^{5}}

by the common factor:

{(y^{5})}^{5}

to get the new expression:

y^{5}

\frac{{(x^{3})}^{6} \cdot y^{5} \cdot {(z^{5})}^{6}}{{(x^{5})}^{5} \cdot z^{5}}

ⓘ A power of a power multiplies the exponents, (a^n)^m = a^(n*m):

{(x^{3})}^{6}

x^{3 \cdot 6}

{(z^{5})}^{6}

z^{5 \cdot 6}

{(x^{5})}^{5}

x^{5 \cdot 5}

\frac{x^{3 \cdot 6} y^{5} z^{5 \cdot 6}}{x^{5 \cdot 5} z^{5}}

ⅰ

3 \cdot 6

18

■

5 \cdot 6

30

■

5 \cdot 5

25

\frac{x^{18} y^{5} z^{30}}{x^{25} z^{5}}

The fraction:

\frac{x^{18}}{x^{25}}

simplifies by the common factor:

x^{18}

into the new quotient:

\frac{1}{x^{7}}

The fraction:

\frac{z^{30}}{z^{5}}

simplifies by the common factor:

z^{5}

into the new expression:

z^{25}

▶Simplified form:

\frac{y^{5} z^{25}}{x^{7}}