Algebra Examples

$\frac{{(- 3 x^{2} y^{3})}^{2} {(4 x^{5} y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{{(- 3 x^{2})}^{2} {(y^{3})}^{2} {(4 x^{5} y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.2

Apply the product rule to $4 x^{5} y^{2}$ .

$\frac{{(- 3 x^{2})}^{2} {(y^{3})}^{2} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.3

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

$\frac{{(- 3)}^{2} {(x^{2})}^{2} {(y^{3})}^{2} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.4

Raise $- 3$ to the power of $2$ .

$\frac{9 {(x^{2})}^{2} {(y^{3})}^{2} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

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

$\frac{9 x^{2 \cdot 2} {(y^{3})}^{2} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.5.2

Multiply $2$ by $2$ .

$\frac{9 x^{4} {(y^{3})}^{2} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.6

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

Tap for more steps...

Step 1.6.1

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

$\frac{9 x^{4} y^{3 \cdot 2} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.6.2

Multiply $3$ by $2$ .

$\frac{9 x^{4} y^{6} {(4 x^{5})}^{3} {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.7

Apply the product rule to $4 x^{5}$ .

$\frac{9 x^{4} y^{6} (4^{3} {(x^{5})}^{3}) {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.8

Raise $4$ to the power of $3$ .

$\frac{9 x^{4} y^{6} (64 {(x^{5})}^{3}) {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.9

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

Tap for more steps...

Step 1.9.1

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

$\frac{9 x^{4} y^{6} (64 x^{5 \cdot 3}) {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.9.2

Multiply $5$ by $3$ .

$\frac{9 x^{4} y^{6} (64 x^{15}) {(y^{2})}^{3}}{288 x^{5} y^{8}}$

Step 1.10

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

Tap for more steps...

Step 1.10.1

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

$\frac{9 x^{4} y^{6} (64 x^{15}) y^{2 \cdot 3}}{288 x^{5} y^{8}}$

Step 1.10.2

Multiply $2$ by $3$ .

$\frac{9 x^{4} y^{6} (64 x^{15}) y^{6}}{288 x^{5} y^{8}}$

$\frac{9 x^{4} y^{6} \cdot 64 x^{15} y^{6}}{288 x^{5} y^{8}}$

Step 1.11

Combine exponents.

Tap for more steps...

Step 1.11.1

Multiply $64$ by $9$ .

$\frac{576 x^{4} y^{6} x^{15} y^{6}}{288 x^{5} y^{8}}$

Step 1.11.2

Multiply $x^{4}$ by $x^{15}$ by adding the exponents.

Tap for more steps...

Step 1.11.2.1

Move $x^{15}$ .

$\frac{576 (x^{15} x^{4}) y^{6} y^{6}}{288 x^{5} y^{8}}$

Step 1.11.2.2

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

$\frac{576 x^{15 + 4} y^{6} y^{6}}{288 x^{5} y^{8}}$

Step 1.11.2.3

Add $15$ and $4$ .

$\frac{576 x^{19} y^{6} y^{6}}{288 x^{5} y^{8}}$

Step 1.11.3

Multiply $y^{6}$ by $y^{6}$ by adding the exponents.

Tap for more steps...

Step 1.11.3.1

Move $y^{6}$ .

$\frac{576 x^{19} (y^{6} y^{6})}{288 x^{5} y^{8}}$

Step 1.11.3.2

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

$\frac{576 x^{19} y^{6 + 6}}{288 x^{5} y^{8}}$

Step 1.11.3.3

Add $6$ and $6$ .

$\frac{576 x^{19} y^{12}}{288 x^{5} y^{8}}$

Step 2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.1

Cancel the common factor of $576$ and $288$ .

Tap for more steps...

Step 2.1.1

Factor $288$ out of $576 x^{19} y^{12}$ .

$\frac{288 (2 x^{19} y^{12})}{288 x^{5} y^{8}}$

Step 2.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.2.1

Factor $288$ out of $288 x^{5} y^{8}$ .

$\frac{288 (2 x^{19} y^{12})}{288 (x^{5} y^{8})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{288 (2 x^{19} y^{12})}{288 (x^{5} y^{8})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{2 x^{19} y^{12}}{x^{5} y^{8}}$

Step 2.2

Cancel the common factor of $x^{19}$ and $x^{5}$ .

Tap for more steps...

Step 2.2.1

Factor $x^{5}$ out of $2 x^{19} y^{12}$ .

$\frac{x^{5} (2 x^{14} y^{12})}{x^{5} y^{8}}$

Step 2.2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.2.1

Factor $x^{5}$ out of $x^{5} y^{8}$ .

$\frac{x^{5} (2 x^{14} y^{12})}{x^{5} (y^{8})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{x^{5} (2 x^{14} y^{12})}{x^{5} y^{8}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{2 x^{14} y^{12}}{y^{8}}$

Step 2.3

Cancel the common factor of $y^{12}$ and $y^{8}$ .

Tap for more steps...

Step 2.3.1

Factor $y^{8}$ out of $2 x^{14} y^{12}$ .

$\frac{y^{8} (2 x^{14} y^{4})}{y^{8}}$

Step 2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.2.1

Multiply by $1$ .

$\frac{y^{8} (2 x^{14} y^{4})}{y^{8} \cdot 1}$

Step 2.3.2.2

Cancel the common factor.

$\frac{y^{8} (2 x^{14} y^{4})}{y^{8} \cdot 1}$

Step 2.3.2.3

Rewrite the expression.

$\frac{2 x^{14} y^{4}}{1}$

Step 2.3.2.4

Divide $2 x^{14} y^{4}$ by $1$ .

$2 x^{14} y^{4}$