Algebra Examples

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

Step 1

Multiply $x^{- 2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $x$ .

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

Step 1.2

Multiply $x$ by $x^{- 2}$ .

Tap for more steps...

Step 1.2.1

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

$\frac{3 (x^{1} x^{- 2}) y^{3} (5 y^{- 8})}{{(x^{- 3})}^{4} y^{- 2}}$

Step 1.2.2

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

$\frac{3 x^{1 - 2} y^{3} (5 y^{- 8})}{{(x^{- 3})}^{4} y^{- 2}}$

Step 1.3

Subtract $2$ from $1$ .

$\frac{3 x^{- 1} y^{3} (5 y^{- 8})}{{(x^{- 3})}^{4} y^{- 2}}$

Step 2

Multiply $y^{3}$ by $y^{- 8}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $y^{- 8}$ .

$\frac{3 x^{- 1} (y^{- 8} y^{3}) \cdot 5}{{(x^{- 3})}^{4} y^{- 2}}$

Step 2.2

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

$\frac{3 x^{- 1} y^{- 8 + 3} \cdot 5}{{(x^{- 3})}^{4} y^{- 2}}$

Step 2.3

Add $- 8$ and $3$ .

$\frac{3 x^{- 1} y^{- 5} \cdot 5}{{(x^{- 3})}^{4} y^{- 2}}$

Step 3

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4

Move $y^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 5

Multiply $y^{- 2}$ by $y^{5}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $y^{5}$ .

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

Step 5.2

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

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

Step 5.3

Subtract $2$ from $5$ .

$\frac{3 \cdot 5}{{(x^{- 3})}^{4} y^{3} x}$

Step 6

Multiply $3$ by $5$ .

$\frac{15}{{(x^{- 3})}^{4} y^{3} x}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

Multiply the exponents in ${(x^{- 3})}^{4}$ .

Tap for more steps...

Step 7.1.1

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

$\frac{15}{x^{- 3 \cdot 4} y^{3} x}$

Step 7.1.2

Multiply $- 3$ by $4$ .

$\frac{15}{x^{- 12} y^{3} x}$

Step 7.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{15}{\frac{1}{x^{12}} y^{3} x}$

Step 7.3

Combine exponents.

Tap for more steps...

Step 7.3.1

Combine $\frac{1}{x^{12}}$ and $y^{3}$ .

$\frac{15}{\frac{y^{3}}{x^{12}} x}$

Step 7.3.2

Combine $\frac{y^{3}}{x^{12}}$ and $x$ .

$\frac{15}{\frac{y^{3} x}{x^{12}}}$

Step 7.4

Reduce the expression $\frac{y^{3} x}{x^{12}}$ by cancelling the common factors.

Tap for more steps...

Step 7.4.1

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

$\frac{15}{\frac{x y^{3}}{x^{12}}}$

Step 7.4.2

Factor $x$ out of $x^{12}$ .

$\frac{15}{\frac{x y^{3}}{x \cdot x^{11}}}$

Step 7.4.3

Cancel the common factor.

$\frac{15}{\frac{x y^{3}}{x \cdot x^{11}}}$

Step 7.4.4

Rewrite the expression.

$\frac{15}{\frac{y^{3}}{x^{11}}}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$15 \frac{x^{11}}{y^{3}}$

Step 9

Combine $15$ and $\frac{x^{11}}{y^{3}}$ .

$\frac{15 x^{11}}{y^{3}}$