Finite Math Examples

$\frac{8^{2}}{2^{x}} = 4$

Step 1

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

$8^{2} \cdot 2^{- x} = 4$

Step 2

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{2} \cdot 2^{- x} = 4$

Step 3

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

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Step 3.1

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

$2^{3 \cdot 2} \cdot 2^{- x} = 4$

Step 3.2

Multiply $3$ by $2$ .

$2^{6} \cdot 2^{- x} = 4$

Step 4

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

$2^{6 - x} = 4$

Step 5

Create equivalent expressions in the equation that all have equal bases.

$2^{6 - x} = 2^{2}$

Step 6

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

$6 - x = 2$

Step 7

Solve for $x$ .

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Step 7.1

Move all terms not containing $x$ to the right side of the equation.

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Step 7.1.1

Subtract $6$ from both sides of the equation.

$- x = 2 - 6$

Step 7.1.2

Subtract $6$ from $2$ .

$- x = - 4$

Step 7.2

Divide each term in $- x = - 4$ by $- 1$ and simplify.

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Step 7.2.1

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Step 7.2.2

Simplify the left side.

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Step 7.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Step 7.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Step 7.2.3

Simplify the right side.

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Step 7.2.3.1

Divide $- 4$ by $- 1$ .

$x = 4$