Precalculus Examples

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

Step 1

Multiply $4^{3 k - 2}$ by $4^{- 2 k}$ 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.

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

Step 1.2

Subtract $2 k$ from $3 k$ .

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

Step 2

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

$k - 2 = 3 k$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

Subtract $3 k$ from both sides of the equation.

$k - 2 - 3 k = 0$

Step 3.1.2

Subtract $3 k$ from $k$ .

$- 2 k - 2 = 0$

Step 3.2

Add $2$ to both sides of the equation.

$- 2 k = 2$

Step 3.3

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

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Step 3.3.1

Divide each term in $- 2 k = 2$ by $- 2$ .

$\frac{- 2 k}{- 2} = \frac{2}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 k}{- 2} = \frac{2}{- 2}$

Step 3.3.2.1.2

Divide $k$ by $1$ .

$k = \frac{2}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $2$ by $- 2$ .

$k = - 1$