Algebra Examples

$(- x^{3} y z^{- 1}) {(2 x^{5} y^{- 1} z^{- 3})}^{3}$

Step 1

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

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

Step 2

Multiply $- x^{3} y \frac{1}{z}$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 3

Rewrite $- 1 \frac{x^{3} y}{z}$ as $- \frac{x^{3} y}{z}$ .

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

Step 4

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

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

Step 5

Multiply $2 x^{5} \frac{1}{y}$ .

Tap for more steps...

Step 5.1

Combine $2$ and $\frac{1}{y}$ .

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

Step 5.2

Combine $x^{5}$ and $\frac{2}{y}$ .

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

Step 6

Move $2$ to the left of $x^{5}$ .

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

Step 7

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

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

Step 8

Combine.

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

Step 9

Multiply $2$ by $1$ .

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

Step 10

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 10.1

Apply the product rule to $\frac{2 x^{5}}{y z^{3}}$ .

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

Step 10.2

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

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

Step 10.3

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

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

Step 11

Simplify the numerator.

Tap for more steps...

Step 11.1

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

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

Step 11.2

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

Tap for more steps...

Step 11.2.1

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

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

Step 11.2.2

Multiply $5$ by $3$ .

$- \frac{x^{3} y}{z} \cdot \frac{8 x^{15}}{y^{3} {(z^{3})}^{3}}$

Step 12

Simplify terms.

Tap for more steps...

Step 12.1

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

Tap for more steps...

Step 12.1.1

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

$- \frac{x^{3} y}{z} \cdot \frac{8 x^{15}}{y^{3} z^{3 \cdot 3}}$

Step 12.1.2

Multiply $3$ by $3$ .

$- \frac{x^{3} y}{z} \cdot \frac{8 x^{15}}{y^{3} z^{9}}$

Step 12.2

Cancel the common factor of $y$ .

Tap for more steps...

Step 12.2.1

Move the leading negative in $- \frac{x^{3} y}{z}$ into the numerator.

$\frac{- x^{3} y}{z} \cdot \frac{8 x^{15}}{y^{3} z^{9}}$

Step 12.2.2

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

$\frac{y (- x^{3})}{z} \cdot \frac{8 x^{15}}{y^{3} z^{9}}$

Step 12.2.3

Factor $y$ out of $y^{3} z^{9}$ .

$\frac{y (- x^{3})}{z} \cdot \frac{8 x^{15}}{y (y^{2} z^{9})}$

Step 12.2.4

Cancel the common factor.

$\frac{y (- x^{3})}{z} \cdot \frac{8 x^{15}}{y (y^{2} z^{9})}$

Step 12.2.5

Rewrite the expression.

$\frac{- x^{3}}{z} \cdot \frac{8 x^{15}}{y^{2} z^{9}}$

Step 12.3

Multiply $\frac{- x^{3}}{z}$ by $\frac{8 x^{15}}{y^{2} z^{9}}$ .

$\frac{- x^{3} (8 x^{15})}{z (y^{2} z^{9})}$

Step 12.4

Multiply $8$ by $- 1$ .

$\frac{- 8 x^{3} x^{15}}{z (y^{2} z^{9})}$

Step 13

Multiply $x^{3}$ by $x^{15}$ by adding the exponents.

Tap for more steps...

Step 13.1

Move $x^{15}$ .

$\frac{- 8 (x^{15} x^{3})}{z (y^{2} z^{9})}$

Step 13.2

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

$\frac{- 8 x^{15 + 3}}{z (y^{2} z^{9})}$

Step 13.3

Add $15$ and $3$ .

$\frac{- 8 x^{18}}{z (y^{2} z^{9})}$

Step 14

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

$\frac{- 8 x^{18}}{y^{2} (z^{1} z^{9})}$

Step 15

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

$\frac{- 8 x^{18}}{y^{2} z^{1 + 9}}$

Step 16

Add $1$ and $9$ .

$\frac{- 8 x^{18}}{y^{2} z^{10}}$

Step 17

Move the negative in front of the fraction.

$- \frac{8 x^{18}}{y^{2} z^{10}}$