Pre-Algebra Examples

$\frac{(7 x^{4} y^{5}) (9 x^{3} y^{3})}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 1

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $x^{3}$ .

$\frac{7 (x^{3} x^{4}) y^{5} (9 y^{3})}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 1.2

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

$\frac{7 x^{3 + 4} y^{5} (9 y^{3})}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 1.3

Add $3$ and $4$ .

$\frac{7 x^{7} y^{5} (9 y^{3})}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 2

Multiply $y^{5}$ by $y^{3}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $y^{3}$ .

$\frac{7 x^{7} (y^{3} y^{5}) \cdot 9}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 2.2

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

$\frac{7 x^{7} y^{3 + 5} \cdot 9}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 2.3

Add $3$ and $5$ .

$\frac{7 x^{7} y^{8} \cdot 9}{(21 x y^{5}) (3 x^{3} y^{8})}$

Step 3

Multiply $x$ by $x^{3}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $x^{3}$ .

$\frac{7 x^{7} y^{8} \cdot 9}{21 (x^{3} x) y^{5} (3 y^{8})}$

Step 3.2

Multiply $x^{3}$ by $x$ .

Tap for more steps...

Step 3.2.1

Raise $x$ to the power of $1$ .

$\frac{7 x^{7} y^{8} \cdot 9}{21 (x^{3} x^{1}) y^{5} (3 y^{8})}$

Step 3.2.2

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

$\frac{7 x^{7} y^{8} \cdot 9}{21 x^{3 + 1} y^{5} (3 y^{8})}$

Step 3.3

Add $3$ and $1$ .

$\frac{7 x^{7} y^{8} \cdot 9}{21 x^{4} y^{5} (3 y^{8})}$

Step 4

Multiply $y^{5}$ by $y^{8}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $y^{8}$ .

$\frac{7 x^{7} y^{8} \cdot 9}{21 x^{4} (y^{8} y^{5}) \cdot 3}$

Step 4.2

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

$\frac{7 x^{7} y^{8} \cdot 9}{21 x^{4} y^{8 + 5} \cdot 3}$

Step 4.3

Add $8$ and $5$ .

$\frac{7 x^{7} y^{8} \cdot 9}{21 x^{4} y^{13} \cdot 3}$

Step 5

Cancel the common factor of $7$ and $21$ .

Tap for more steps...

Step 5.1

Factor $7$ out of $7 x^{7} y^{8} \cdot 9$ .

$\frac{7 (x^{7} y^{8} \cdot 9)}{21 x^{4} y^{13} \cdot 3}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $7$ out of $21 x^{4} y^{13} \cdot 3$ .

$\frac{7 (x^{7} y^{8} \cdot 9)}{7 (3 x^{4} y^{13} \cdot 3)}$

Step 5.2.2

Cancel the common factor.

$\frac{7 (x^{7} y^{8} \cdot 9)}{7 (3 x^{4} y^{13} \cdot 3)}$

Step 5.2.3

Rewrite the expression.

$\frac{x^{7} y^{8} \cdot 9}{3 x^{4} y^{13} \cdot 3}$

Step 6

Cancel the common factor of $x^{7}$ and $x^{4}$ .

Tap for more steps...

Step 6.1

Factor $x^{4}$ out of $x^{7} y^{8} \cdot 9$ .

$\frac{x^{4} (x^{3} y^{8} \cdot 9)}{3 x^{4} y^{13} \cdot 3}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $x^{4}$ out of $3 x^{4} y^{13} \cdot 3$ .

$\frac{x^{4} (x^{3} y^{8} \cdot 9)}{x^{4} (3 y^{13} \cdot 3)}$

Step 6.2.2

Cancel the common factor.

$\frac{x^{4} (x^{3} y^{8} \cdot 9)}{x^{4} (3 y^{13} \cdot 3)}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{3} y^{8} \cdot 9}{3 y^{13} \cdot 3}$

Step 7

Cancel the common factor of $y^{8}$ and $y^{13}$ .

Tap for more steps...

Step 7.1

Factor $y^{8}$ out of $x^{3} y^{8} \cdot 9$ .

$\frac{y^{8} (x^{3} \cdot 9)}{3 y^{13} \cdot 3}$

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $y^{8}$ out of $3 y^{13} \cdot 3$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{x^{3} \cdot 9}{3 y^{5} \cdot 3}$

Step 8

Cancel the common factor of $9$ and $3$ .

Tap for more steps...

Step 8.1

Factor $3$ out of $x^{3} \cdot 9$ .

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

Step 8.2

Cancel the common factors.

Tap for more steps...

Step 8.2.1

Factor $3$ out of $3 y^{5} \cdot 3$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$\frac{x^{3} \cdot 3}{y^{5} \cdot 3}$

Step 9

Cancel the common factor of $3$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$\frac{x^{3} \cdot 3}{y^{5} \cdot 3}$

Step 9.2

Rewrite the expression.

$\frac{x^{3}}{y^{5}}$