Basic Math Examples

$3^{4} \div 3^{n} = 9$

Step 1

Move $3^{n}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3^{4} \cdot 3^{- n} = 9$

Step 2

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

$3^{4 - n} = 9$

Step 3

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

$3^{4 - n} = 3^{2}$

Step 4

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

$4 - n = 2$

Step 5

Solve for $n$ .

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Step 5.1

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

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Step 5.1.1

Subtract $4$ from both sides of the equation.

$- n = 2 - 4$

Step 5.1.2

Subtract $4$ from $2$ .

$- n = - 2$

Step 5.2

Divide each term in $- n = - 2$ by $- 1$ and simplify.

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Step 5.2.1

Divide each term in $- n = - 2$ by $- 1$ .

$\frac{- n}{- 1} = \frac{- 2}{- 1}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{- 2}{- 1}$

Step 5.2.2.2

Divide $n$ by $1$ .

$n = \frac{- 2}{- 1}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 2$ by $- 1$ .

$n = 2$