Finite Math Examples

$\frac{a^{6} x {(a^{3})}^{2} x a^{- 7}}{a^{- 5}}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.1

Move $x$ .

$\frac{a^{6} (x \cdot x) {(a^{3})}^{2} a^{- 7}}{a^{- 5}}$

Step 1.1.2

Multiply $x$ by $x$ .

$\frac{a^{6} x^{2} {(a^{3})}^{2} a^{- 7}}{a^{- 5}}$

Step 1.2

Multiply $a^{6}$ by $a^{- 7}$ by adding the exponents.

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Step 1.2.1

Move $a^{- 7}$ .

$\frac{a^{- 7} a^{6} x^{2} {(a^{3})}^{2}}{a^{- 5}}$

Step 1.2.2

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

$\frac{a^{- 7 + 6} x^{2} {(a^{3})}^{2}}{a^{- 5}}$

Step 1.2.3

Add $- 7$ and $6$ .

$\frac{a^{- 1} x^{2} {(a^{3})}^{2}}{a^{- 5}}$

Step 1.3

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

$a^{- 1} x^{2} {(a^{3})}^{2} a^{5}$

Step 1.4

Multiply $a^{- 1}$ by $a^{5}$ by adding the exponents.

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Step 1.4.1

Move $a^{5}$ .

$a^{5} a^{- 1} x^{2} {(a^{3})}^{2}$

Step 1.4.2

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

$a^{5 - 1} x^{2} {(a^{3})}^{2}$

Step 1.4.3

Subtract $1$ from $5$ .

$a^{4} x^{2} {(a^{3})}^{2}$

Step 1.5

Multiply the exponents in ${(a^{3})}^{2}$ .

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Step 1.5.1

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

$a^{4} x^{2} a^{3 \cdot 2}$

Step 1.5.2

Multiply $3$ by $2$ .

$a^{4} x^{2} a^{6}$

Step 1.6

Multiply $a^{4}$ by $a^{6}$ by adding the exponents.

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Step 1.6.1

Move $a^{6}$ .

$a^{6} a^{4} x^{2}$

Step 1.6.2

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

$a^{6 + 4} x^{2}$

Step 1.6.3

Add $6$ and $4$ .

$a^{10} x^{2}$

Step 2

The largest exponent is the degree of the polynomial.

$12$