Finite Math Examples

${(\frac{4 x^{- 1} y^{- 40}}{2^{- 2} z^{4} y^{- 10}})}^{- 2}$

Step 1

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

${(\frac{4 y^{- 40}}{2^{- 2} z^{4} y^{- 10} x})}^{- 2}$

Step 2

Move $y^{- 40}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{4}{2^{- 2} z^{4} y^{- 10} x y^{40}})}^{- 2}$

Step 3

Multiply $y^{- 10}$ by $y^{40}$ by adding the exponents.

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Step 3.1

Move $y^{40}$ .

${(\frac{4}{2^{- 2} z^{4} (y^{40} y^{- 10}) x})}^{- 2}$

Step 3.2

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

${(\frac{4}{2^{- 2} z^{4} y^{40 - 10} x})}^{- 2}$

Step 3.3

Subtract $10$ from $40$ .

${(\frac{4}{2^{- 2} z^{4} y^{30} x})}^{- 2}$

Step 4

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

${(\frac{4 \cdot 2^{2}}{z^{4} y^{30} x})}^{- 2}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $4$ as $2^{2}$ .

${(\frac{2^{2} \cdot 2^{2}}{z^{4} y^{30} x})}^{- 2}$

Step 5.2

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

${(\frac{2^{2 + 2}}{z^{4} y^{30} x})}^{- 2}$

Step 5.3

Add $2$ and $2$ .

${(\frac{2^{4}}{z^{4} y^{30} x})}^{- 2}$

Step 6

Raise $2$ to the power of $4$ .

${(\frac{16}{z^{4} y^{30} x})}^{- 2}$

Step 7

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{z^{4} y^{30} x}{16})}^{2}$

Step 8

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

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Step 8.1

Apply the product rule to $\frac{z^{4} y^{30} x}{16}$ .

$\frac{{(z^{4} y^{30} x)}^{2}}{16^{2}}$

Step 8.2

Apply the product rule to $z^{4} y^{30} x$ .

$\frac{{(z^{4} y^{30})}^{2} x^{2}}{16^{2}}$

Step 8.3

Apply the product rule to $z^{4} y^{30}$ .

$\frac{{(z^{4})}^{2} {(y^{30})}^{2} x^{2}}{16^{2}}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply the exponents in ${(z^{4})}^{2}$ .

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Step 9.1.1

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

$\frac{z^{4 \cdot 2} {(y^{30})}^{2} x^{2}}{16^{2}}$

Step 9.1.2

Multiply $4$ by $2$ .

$\frac{z^{8} {(y^{30})}^{2} x^{2}}{16^{2}}$

Step 9.2

Multiply the exponents in ${(y^{30})}^{2}$ .

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Step 9.2.1

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

$\frac{z^{8} y^{30 \cdot 2} x^{2}}{16^{2}}$

Step 9.2.2

Multiply $30$ by $2$ .

$\frac{z^{8} y^{60} x^{2}}{16^{2}}$

Step 10

Raise $16$ to the power of $2$ .

$\frac{z^{8} y^{60} x^{2}}{256}$