Evaluate ((3x^5y^3)^5)/((6x^10y^7)^2)

$\frac{{(3 x^{5} y^{3})}^{5}}{{(6 x^{10} y^{7})}^{2}}$

Simplify the numerator.

Apply the product rule to $3 x^{5} y^{3}$ .

$\frac{{(3 x^{5})}^{5} {(y^{3})}^{5}}{{(6 x^{10} y^{7})}^{2}}$

Apply the product rule to $3 x^{5}$ .

$\frac{3^{5} {(x^{5})}^{5} {(y^{3})}^{5}}{{(6 x^{10} y^{7})}^{2}}$

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

$\frac{243 {(x^{5})}^{5} {(y^{3})}^{5}}{{(6 x^{10} y^{7})}^{2}}$

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

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

$\frac{243 x^{5 \cdot 5} {(y^{3})}^{5}}{{(6 x^{10} y^{7})}^{2}}$

Multiply $5$ by $5$ .

$\frac{243 x^{25} {(y^{3})}^{5}}{{(6 x^{10} y^{7})}^{2}}$

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

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

$\frac{243 x^{25} y^{3 \cdot 5}}{{(6 x^{10} y^{7})}^{2}}$

Multiply $3$ by $5$ .

$\frac{243 x^{25} y^{15}}{{(6 x^{10} y^{7})}^{2}}$

Simplify the denominator.

Apply the product rule to $6 x^{10} y^{7}$ .

$\frac{243 x^{25} y^{15}}{{(6 x^{10})}^{2} {(y^{7})}^{2}}$

Apply the product rule to $6 x^{10}$ .

$\frac{243 x^{25} y^{15}}{6^{2} {(x^{10})}^{2} {(y^{7})}^{2}}$

Raise $6$ to the power of $2$ .

$\frac{243 x^{25} y^{15}}{36 {(x^{10})}^{2} {(y^{7})}^{2}}$

Multiply the exponents in ${(x^{10})}^{2}$ .

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

$\frac{243 x^{25} y^{15}}{36 x^{10 \cdot 2} {(y^{7})}^{2}}$

Multiply $10$ by $2$ .

$\frac{243 x^{25} y^{15}}{36 x^{20} {(y^{7})}^{2}}$

Multiply the exponents in ${(y^{7})}^{2}$ .

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

$\frac{243 x^{25} y^{15}}{36 x^{20} y^{7 \cdot 2}}$

Multiply $7$ by $2$ .

$\frac{243 x^{25} y^{15}}{36 x^{20} y^{14}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $243$ and $36$ .

Factor $9$ out of $243 x^{25} y^{15}$ .

$\frac{9 (27 x^{25} y^{15})}{36 x^{20} y^{14}}$

Cancel the common factors.

Factor $9$ out of $36 x^{20} y^{14}$ .

$\frac{9 (27 x^{25} y^{15})}{9 (4 x^{20} y^{14})}$

Cancel the common factor.

$\frac{9 (27 x^{25} y^{15})}{9 (4 x^{20} y^{14})}$

Rewrite the expression.

$\frac{27 x^{25} y^{15}}{4 x^{20} y^{14}}$

Cancel the common factor of $x^{25}$ and $x^{20}$ .

Factor $x^{20}$ out of $27 x^{25} y^{15}$ .

$\frac{x^{20} (27 x^{5} y^{15})}{4 x^{20} y^{14}}$

Cancel the common factors.

Factor $x^{20}$ out of $4 x^{20} y^{14}$ .

$\frac{x^{20} (27 x^{5} y^{15})}{x^{20} (4 y^{14})}$

Cancel the common factor.

$\frac{x^{20} (27 x^{5} y^{15})}{x^{20} (4 y^{14})}$

Rewrite the expression.

$\frac{27 x^{5} y^{15}}{4 y^{14}}$

Cancel the common factor of $y^{15}$ and $y^{14}$ .

Factor $y^{14}$ out of $27 x^{5} y^{15}$ .

$\frac{y^{14} (27 x^{5} y)}{4 y^{14}}$

Cancel the common factors.

Factor $y^{14}$ out of $4 y^{14}$ .

$\frac{y^{14} (27 x^{5} y)}{y^{14} \cdot 4}$

Cancel the common factor.

$\frac{y^{14} (27 x^{5} y)}{y^{14} \cdot 4}$

Rewrite the expression.

$\frac{27 x^{5} y}{4}$

Evaluate ((3x^5y^3)^5)/((6x^10y^7)^2)

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