Algebra Examples

${(\frac{3 x^{3} y^{0}}{x^{- 2}})}^{4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 1

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3 x^{3} y^{0} x^{2})}^{4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 2.1

Move $x^{2}$ .

${(3 (x^{2} x^{3}) y^{0})}^{4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 2.2

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

${(3 x^{2 + 3} y^{0})}^{4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 2.3

Add $2$ and $3$ .

${(3 x^{5} y^{0})}^{4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 3

Simplify $3 x^{5} y^{0}$ .

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

Step 4

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

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

Step 5

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

$81 {(x^{5})}^{4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 6

Multiply the exponents in ${(x^{5})}^{4}$ .

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Step 6.1

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

$81 x^{5 \cdot 4} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 6.2

Multiply $5$ by $4$ .

$81 x^{20} \cdot {(\frac{y^{2} x^{- 4}}{5 x y^{- 8}})}^{3}$

Step 7

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$81 x^{20} \cdot {(\frac{y^{2}}{5 x y^{- 8} x^{4}})}^{3}$

Step 8

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

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Step 8.1

Move $x^{4}$ .

$81 x^{20} \cdot {(\frac{y^{2}}{5 (x^{4} x) y^{- 8}})}^{3}$

Step 8.2

Multiply $x^{4}$ by $x$ .

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Step 8.2.1

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

$81 x^{20} \cdot {(\frac{y^{2}}{5 (x^{4} x^{1}) y^{- 8}})}^{3}$

Step 8.2.2

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

$81 x^{20} \cdot {(\frac{y^{2}}{5 x^{4 + 1} y^{- 8}})}^{3}$

Step 8.3

Add $4$ and $1$ .

$81 x^{20} \cdot {(\frac{y^{2}}{5 x^{5} y^{- 8}})}^{3}$

Step 9

Move $y^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$81 x^{20} \cdot {(\frac{y^{2} y^{8}}{5 x^{5}})}^{3}$

Step 10

Multiply $y^{2}$ by $y^{8}$ by adding the exponents.

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Step 10.1

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

$81 x^{20} \cdot {(\frac{y^{2 + 8}}{5 x^{5}})}^{3}$

Step 10.2

Add $2$ and $8$ .

$81 x^{20} \cdot {(\frac{y^{10}}{5 x^{5}})}^{3}$

Step 11

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

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Step 11.1

Apply the product rule to $\frac{y^{10}}{5 x^{5}}$ .

$81 x^{20} \cdot \frac{{(y^{10})}^{3}}{{(5 x^{5})}^{3}}$

Step 11.2

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

$81 x^{20} \cdot \frac{{(y^{10})}^{3}}{5^{3} {(x^{5})}^{3}}$

Step 12

Multiply the exponents in ${(y^{10})}^{3}$ .

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Step 12.1

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

$81 x^{20} \cdot \frac{y^{10 \cdot 3}}{5^{3} {(x^{5})}^{3}}$

Step 12.2

Multiply $10$ by $3$ .

$81 x^{20} \cdot \frac{y^{30}}{5^{3} {(x^{5})}^{3}}$

Step 13

Simplify the denominator.

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Step 13.1

Raise $5$ to the power of $3$ .

$81 x^{20} \cdot \frac{y^{30}}{125 {(x^{5})}^{3}}$

Step 13.2

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

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Step 13.2.1

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

$81 x^{20} \cdot \frac{y^{30}}{125 x^{5 \cdot 3}}$

Step 13.2.2

Multiply $5$ by $3$ .

$81 x^{20} \cdot \frac{y^{30}}{125 x^{15}}$

Step 14

Simplify terms.

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Step 14.1

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

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Step 14.1.1

Factor $x^{15}$ out of $81 x^{20}$ .

$x^{15} (81 x^{5}) \cdot \frac{y^{30}}{125 x^{15}}$

Step 14.1.2

Factor $x^{15}$ out of $125 x^{15}$ .

$x^{15} (81 x^{5}) \cdot \frac{y^{30}}{x^{15} \cdot 125}$

Step 14.1.3

Cancel the common factor.

$x^{15} (81 x^{5}) \cdot \frac{y^{30}}{x^{15} \cdot 125}$

Step 14.1.4

Rewrite the expression.

$81 x^{5} \cdot \frac{y^{30}}{125}$

Step 14.2

Combine $81$ and $\frac{y^{30}}{125}$ .

$x^{5} \cdot \frac{81 y^{30}}{125}$

Step 14.3

Combine $x^{5}$ and $\frac{81 y^{30}}{125}$ .

$\frac{x^{5} (81 y^{30})}{125}$

Step 14.4

Move $81$ to the left of $x^{5}$ .

$\frac{81 x^{5} y^{30}}{125}$