Finite Math Examples

${(\frac{{(8 x^{21})}^{0} y^{- 3} x^{8}}{y^{- 9} x^{- 1}})}^{- 6}$

Step 1

Move $y^{- 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{{(8 x^{21})}^{0} y^{- 3} x^{8} y^{9}}{x^{- 1}})}^{- 6}$

Step 2

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

${({(8 x^{21})}^{0} y^{- 3} x^{8} y^{9} x)}^{- 6}$

Step 3

Multiply $y^{- 3}$ by $y^{9}$ by adding the exponents.

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Step 3.1

Move $y^{9}$ .

${({(8 x^{21})}^{0} (y^{9} y^{- 3}) x^{8} x)}^{- 6}$

Step 3.2

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

${({(8 x^{21})}^{0} y^{9 - 3} x^{8} x)}^{- 6}$

Step 3.3

Subtract $3$ from $9$ .

${({(8 x^{21})}^{0} y^{6} x^{8} x)}^{- 6}$

Step 4

Simplify ${(8 x^{21})}^{0} y^{6} x^{8}$ .

${(y^{6} x^{8} x)}^{- 6}$

Step 5

Multiply $x^{8}$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

${(y^{6} (x \cdot x^{8}))}^{- 6}$

Step 5.2

Multiply $x$ by $x^{8}$ .

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Step 5.2.1

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

${(y^{6} (x^{1} x^{8}))}^{- 6}$

Step 5.2.2

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

${(y^{6} x^{1 + 8})}^{- 6}$

Step 5.3

Add $1$ and $8$ .

${(y^{6} x^{9})}^{- 6}$

Step 6

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

$\frac{1}{{(y^{6} x^{9})}^{6}}$

Step 7

Simplify the denominator.

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Step 7.1

Apply the product rule to $y^{6} x^{9}$ .

$\frac{1}{{(y^{6})}^{6} {(x^{9})}^{6}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{1}{y^{6 \cdot 6} {(x^{9})}^{6}}$

Step 7.2.2

Multiply $6$ by $6$ .

$\frac{1}{y^{36} {(x^{9})}^{6}}$

Step 7.3

Multiply the exponents in ${(x^{9})}^{6}$ .

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Step 7.3.1

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

$\frac{1}{y^{36} x^{9 \cdot 6}}$

Step 7.3.2

Multiply $9$ by $6$ .

$\frac{1}{y^{36} x^{54}}$