Finite Math Examples

${(x^{13})}^{5} \cdot {(x^{- 8})}^{- 5} = {(x^{m})}^{3}$

Step 1

Rewrite the equation as ${(x^{m})}^{3} = {(x^{13})}^{5} \cdot {(x^{- 8})}^{- 5}$ .

${(x^{m})}^{3} = {(x^{13})}^{5} \cdot {(x^{- 8})}^{- 5}$

Step 2

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

$x^{m \cdot 3} = {(x^{13})}^{5} \cdot {(x^{- 8})}^{- 5}$

Step 3

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

$x^{m \cdot 3} = x^{13 \cdot 5} \cdot {(x^{- 8})}^{- 5}$

Step 4

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

$x^{m \cdot 3} = x^{13 \cdot 5} \cdot x^{- 8 \cdot - 5}$

Step 5

Multiply $x^{13 \cdot 5}$ by $x^{- 8 \cdot - 5}$ by adding the exponents.

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Step 5.1

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

$x^{m \cdot 3} = x^{13 \cdot 5 - 8 \cdot - 5}$

Step 5.2

Simplify each term.

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Step 5.2.1

Multiply $13$ by $5$ .

$x^{m \cdot 3} = x^{65 - 8 \cdot - 5}$

Step 5.2.2

Multiply $- 8$ by $- 5$ .

$x^{m \cdot 3} = x^{65 + 40}$

Step 5.3

Add $65$ and $40$ .

$x^{m \cdot 3} = x^{105}$

Step 6

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$m \cdot 3 = 105$

Step 7

Divide each term in $m \cdot 3 = 105$ by $3$ and simplify.

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Step 7.1

Divide each term in $m \cdot 3 = 105$ by $3$ .

$\frac{m \cdot 3}{3} = \frac{105}{3}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $3$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{m \cdot 3}{3} = \frac{105}{3}$

Step 7.2.1.2

Divide $m$ by $1$ .

$m = \frac{105}{3}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $105$ by $3$ .

$m = 35$