Algebra Examples

$16 \cdot 2^{6 m} = 2^{3 m - 8}$

Step 1

Rewrite $16$ as $2^{4}$ .

$2^{4} \cdot 2^{6 m} = 2^{3 m - 8}$

Step 2

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

$2^{4 + 6 m} = 2^{3 m - 8}$

Step 3

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

$4 + 6 m = 3 m - 8$

Step 4

Solve for $m$ .

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Step 4.1

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

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Step 4.1.1

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

$4 + 6 m - 3 m = - 8$

Step 4.1.2

Subtract $3 m$ from $6 m$ .

$4 + 3 m = - 8$

Step 4.2

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

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$3 m = - 8 - 4$

Step 4.2.2

Subtract $4$ from $- 8$ .

$3 m = - 12$

Step 4.3

Divide each term in $3 m = - 12$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 m = - 12$ by $3$ .

$\frac{3 m}{3} = \frac{- 12}{3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 m}{3} = \frac{- 12}{3}$

Step 4.3.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 12}{3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 12$ by $3$ .

$m = - 4$