Precalculus Examples

$5^{- 2 n - 3} = 125$

Step 1

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

$5^{- 2 n - 3} = 5^{3}$

Step 2

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

$- 2 n - 3 = 3$

Step 3

Solve for $n$ .

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Step 3.1

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

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Step 3.1.1

Add $3$ to both sides of the equation.

$- 2 n = 3 + 3$

Step 3.1.2

Add $3$ and $3$ .

$- 2 n = 6$

Step 3.2

Divide each term in $- 2 n = 6$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 n = 6$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{6}{- 2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{6}{- 2}$

Step 3.2.2.1.2

Divide $n$ by $1$ .

$n = \frac{6}{- 2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $6$ by $- 2$ .

$n = - 3$