Algebra Examples

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

Step 1

Move $x^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3 x^{5} y^{4} x^{0} y^{3})}^{2}$

Step 3

Multiply $x^{5}$ by $x^{0}$ by adding the exponents.

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Step 3.1

Move $x^{0}$ .

${(3 (x^{0} x^{5}) y^{4} y^{3})}^{2}$

Step 3.2

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

${(3 x^{0 + 5} y^{4} y^{3})}^{2}$

Step 3.3

Add $0$ and $5$ .

${(3 x^{5} y^{4} y^{3})}^{2}$

Step 4

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

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Step 4.1

Move $y^{3}$ .

${(3 x^{5} (y^{3} y^{4}))}^{2}$

Step 4.2

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

${(3 x^{5} y^{3 + 4})}^{2}$

Step 4.3

Add $3$ and $4$ .

${(3 x^{5} y^{7})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $3 x^{5} y^{7}$ .

${(3 x^{5})}^{2} {(y^{7})}^{2}$

Step 5.2

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

$3^{2} {(x^{5})}^{2} {(y^{7})}^{2}$

Step 6

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

$9 {(x^{5})}^{2} {(y^{7})}^{2}$

Step 7

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 7.1

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

$9 x^{5 \cdot 2} {(y^{7})}^{2}$

Step 7.2

Multiply $5$ by $2$ .

$9 x^{10} {(y^{7})}^{2}$

Step 8

Multiply the exponents in ${(y^{7})}^{2}$ .

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Step 8.1

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

$9 x^{10} y^{7 \cdot 2}$

Step 8.2

Multiply $7$ by $2$ .

$9 x^{10} y^{14}$