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

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

Step 1

Apply the product rule to $\frac{x}{y^{2}}$ .

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

Step 2

Multiply the exponents in ${(y^{2})}^{5}$ .

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

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

Multiply $2$ by $5$ .

$\frac{x^{5}}{y^{10}} {(\frac{x^{2} y^{3}}{z^{2}})}^{3}$

Step 3

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

Apply the product rule to $\frac{x^{2} y^{3}}{z^{2}}$ .

$\frac{x^{5}}{y^{10}} \cdot \frac{{(x^{2} y^{3})}^{3}}{{(z^{2})}^{3}}$

Apply the product rule to $x^{2} y^{3}$ .

$\frac{x^{5}}{y^{10}} \cdot \frac{{(x^{2})}^{3} {(y^{3})}^{3}}{{(z^{2})}^{3}}$

Step 4

Combine.

$\frac{x^{5} ({(x^{2})}^{3} {(y^{3})}^{3})}{y^{10} {(z^{2})}^{3}}$

Step 5

Simplify the numerator.

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$\frac{x^{5} x^{2 \cdot 3} {(y^{3})}^{3}}{y^{10} {(z^{2})}^{3}}$

Multiply $2$ by $3$ .

$\frac{x^{5} x^{6} {(y^{3})}^{3}}{y^{10} {(z^{2})}^{3}}$

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

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

$\frac{x^{5} x^{6} y^{3 \cdot 3}}{y^{10} {(z^{2})}^{3}}$

Multiply $3$ by $3$ .

$\frac{x^{5} x^{6} y^{9}}{y^{10} {(z^{2})}^{3}}$

Multiply $x^{5}$ by $x^{6}$ by adding the exponents.

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

$\frac{x^{5 + 6} y^{9}}{y^{10} {(z^{2})}^{3}}$

Add $5$ and $6$ .

$\frac{x^{11} y^{9}}{y^{10} {(z^{2})}^{3}}$

Step 6

Reduce the expression by cancelling the common factors.

Multiply the exponents in ${(z^{2})}^{3}$ .

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

$\frac{x^{11} y^{9}}{y^{10} z^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{x^{11} y^{9}}{y^{10} z^{6}}$

Cancel the common factor of $y^{9}$ and $y^{10}$ .

Factor $y^{9}$ out of $x^{11} y^{9}$ .

$\frac{y^{9} x^{11}}{y^{10} z^{6}}$

Cancel the common factors.

Factor $y^{9}$ out of $y^{10} z^{6}$ .

$\frac{y^{9} x^{11}}{y^{9} (y z^{6})}$

Cancel the common factor.

$\frac{y^{9} x^{11}}{y^{9} (y z^{6})}$

Rewrite the expression.

$\frac{x^{11}}{y z^{6}}$

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

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