Algebra Examples

$\frac{{(3 x^{5} y^{5})}^{3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

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

$\frac{{(3 x^{5})}^{3} {(y^{5})}^{3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.1.2

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

$\frac{3^{3} {(x^{5})}^{3} {(y^{5})}^{3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.1.3

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

$\frac{27 {(x^{5})}^{3} {(y^{5})}^{3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.1.4

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

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Step 1.1.4.1

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

$\frac{27 x^{5 \cdot 3} {(y^{5})}^{3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.1.4.2

Multiply $5$ by $3$ .

$\frac{27 x^{15} {(y^{5})}^{3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.1.5

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

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Step 1.1.5.1

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

$\frac{27 x^{15} y^{5 \cdot 3}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.1.5.2

Multiply $5$ by $3$ .

$\frac{27 x^{15} y^{15}}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.2

Cancel the common factor of $27$ and $3$ .

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Step 1.2.1

Factor $3$ out of $27 x^{15} y^{15}$ .

$\frac{3 (9 x^{15} y^{15})}{3 x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $3 x^{3} y^{11}$ .

$\frac{3 (9 x^{15} y^{15})}{3 (x^{3} y^{11})} + 4 x^{12} y^{4}$

Step 1.2.2.2

Cancel the common factor.

$\frac{3 (9 x^{15} y^{15})}{3 (x^{3} y^{11})} + 4 x^{12} y^{4}$

Step 1.2.2.3

Rewrite the expression.

$\frac{9 x^{15} y^{15}}{x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.3

Cancel the common factor of $x^{15}$ and $x^{3}$ .

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Step 1.3.1

Factor $x^{3}$ out of $9 x^{15} y^{15}$ .

$\frac{x^{3} (9 x^{12} y^{15})}{x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $x^{3}$ out of $x^{3} y^{11}$ .

$\frac{x^{3} (9 x^{12} y^{15})}{x^{3} (y^{11})} + 4 x^{12} y^{4}$

Step 1.3.2.2

Cancel the common factor.

$\frac{x^{3} (9 x^{12} y^{15})}{x^{3} y^{11}} + 4 x^{12} y^{4}$

Step 1.3.2.3

Rewrite the expression.

$\frac{9 x^{12} y^{15}}{y^{11}} + 4 x^{12} y^{4}$

Step 1.4

Cancel the common factor of $y^{15}$ and $y^{11}$ .

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Step 1.4.1

Factor $y^{11}$ out of $9 x^{12} y^{15}$ .

$\frac{y^{11} (9 x^{12} y^{4})}{y^{11}} + 4 x^{12} y^{4}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Multiply by $1$ .

$\frac{y^{11} (9 x^{12} y^{4})}{y^{11} \cdot 1} + 4 x^{12} y^{4}$

Step 1.4.2.2

Cancel the common factor.

$\frac{y^{11} (9 x^{12} y^{4})}{y^{11} \cdot 1} + 4 x^{12} y^{4}$

Step 1.4.2.3

Rewrite the expression.

$\frac{9 x^{12} y^{4}}{1} + 4 x^{12} y^{4}$

Step 1.4.2.4

Divide $9 x^{12} y^{4}$ by $1$ .

$9 x^{12} y^{4} + 4 x^{12} y^{4}$

Step 2

Add $9 x^{12} y^{4}$ and $4 x^{12} y^{4}$ .

$13 x^{12} y^{4}$