Algebra Examples

$\frac{12^{n}}{12^{5}} = 12^{4}$

Step 1

Move $12^{5}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$12^{n} \cdot 12^{- 5} = 12^{4}$

Step 2

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

$12^{n - 5} = 12^{4}$

Step 3

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

$n - 5 = 4$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$n = 4 + 5$

Step 4.2

Add $4$ and $5$ .

$n = 9$