Precalculus Examples

$6^{- n} \cdot 6^{- 2 n} = 6^{2 - 3 n}$

Step 1

Multiply $6^{- n}$ by $6^{- 2 n}$ by adding the exponents.

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Step 1.1

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

$6^{- n - 2 n} = 6^{2 - 3 n}$

Step 1.2

Subtract $2 n$ from $- n$ .

$6^{- 3 n} = 6^{2 - 3 n}$

Step 2

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

$- 3 n = 2 - 3 n$

Step 3

Solve for $n$ .

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Step 3.1

Move all terms containing $n$ to the left side of the equation.

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Step 3.1.1

Add $3 n$ to both sides of the equation.

$- 3 n + 3 n = 2$

Step 3.1.2

Add $- 3 n$ and $3 n$ .

$0 = 2$

Step 3.2

Since $0 \neq 2$ , there are no solutions.

No solution