Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

Move $x^{3}$ .

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

Step 4.2

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

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

Step 4.3

Add $3$ and $3$ .

${(x^{6} y^{4} z^{5} y^{4} z^{5})}^{- 2}$

Step 5

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

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Step 5.1

Move $y^{4}$ .

${(x^{6} (y^{4} y^{4}) z^{5} z^{5})}^{- 2}$

Step 5.2

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

${(x^{6} y^{4 + 4} z^{5} z^{5})}^{- 2}$

Step 5.3

Add $4$ and $4$ .

${(x^{6} y^{8} z^{5} z^{5})}^{- 2}$

Step 6

Multiply $z^{5}$ by $z^{5}$ by adding the exponents.

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Step 6.1

Move $z^{5}$ .

${(x^{6} y^{8} (z^{5} z^{5}))}^{- 2}$

Step 6.2

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

${(x^{6} y^{8} z^{5 + 5})}^{- 2}$

Step 6.3

Add $5$ and $5$ .

${(x^{6} y^{8} z^{10})}^{- 2}$

Step 7

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

$\frac{1}{{(x^{6} y^{8} z^{10})}^{2}}$

Step 8

Simplify the denominator.

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Step 8.1

Apply the product rule to $x^{6} y^{8} z^{10}$ .

$\frac{1}{{(x^{6} y^{8})}^{2} {(z^{10})}^{2}}$

Step 8.2

Apply the product rule to $x^{6} y^{8}$ .

$\frac{1}{{(x^{6})}^{2} {(y^{8})}^{2} {(z^{10})}^{2}}$

Step 8.3

Multiply the exponents in ${(x^{6})}^{2}$ .

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Step 8.3.1

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

$\frac{1}{x^{6 \cdot 2} {(y^{8})}^{2} {(z^{10})}^{2}}$

Step 8.3.2

Multiply $6$ by $2$ .

$\frac{1}{x^{12} {(y^{8})}^{2} {(z^{10})}^{2}}$

Step 8.4

Multiply the exponents in ${(y^{8})}^{2}$ .

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Step 8.4.1

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

$\frac{1}{x^{12} y^{8 \cdot 2} {(z^{10})}^{2}}$

Step 8.4.2

Multiply $8$ by $2$ .

$\frac{1}{x^{12} y^{16} {(z^{10})}^{2}}$

Step 8.5

Multiply the exponents in ${(z^{10})}^{2}$ .

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Step 8.5.1

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

$\frac{1}{x^{12} y^{16} z^{10 \cdot 2}}$

Step 8.5.2

Multiply $10$ by $2$ .

$\frac{1}{x^{12} y^{16} z^{20}}$