Simplify (5x^5y)^3(x/(5y))^2

${(5 x^{5} y)}^{3} {(\frac{x}{5 y})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $5 x^{5} y$ .

${(5 x^{5})}^{3} y^{3} {(\frac{x}{5 y})}^{2}$

Apply the product rule to $5 x^{5}$ .

$5^{3} {(x^{5})}^{3} y^{3} {(\frac{x}{5 y})}^{2}$

Step 2

Raise $5$ to the power of $3$ .

$125 {(x^{5})}^{3} y^{3} {(\frac{x}{5 y})}^{2}$

Step 3

Multiply the exponents in ${(x^{5})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$125 x^{5 \cdot 3} y^{3} {(\frac{x}{5 y})}^{2}$

Multiply $5$ by $3$ .

$125 x^{15} y^{3} {(\frac{x}{5 y})}^{2}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{x}{5 y}$ .

$125 x^{15} y^{3} \frac{x^{2}}{{(5 y)}^{2}}$

Apply the product rule to $5 y$ .

$125 x^{15} y^{3} \frac{x^{2}}{5^{2} y^{2}}$

Step 5

Raise $5$ to the power of $2$ .

$125 x^{15} y^{3} \frac{x^{2}}{25 y^{2}}$

Step 6

Cancel the common factor of $25 y^{2}$ .

Factor $25 y^{2}$ out of $125 x^{15} y^{3}$ .

$25 y^{2} (5 x^{15} y) \frac{x^{2}}{25 y^{2}}$

Cancel the common factor.

$25 y^{2} (5 x^{15} y) \frac{x^{2}}{25 y^{2}}$

Rewrite the expression.

$5 x^{15} y x^{2}$

Step 7

Multiply $x^{15}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$5 (x^{2} x^{15}) y$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{2 + 15} y$

Add $2$ and $15$ .

$5 x^{17} y$