Algebra Examples

$8 \cdot 2^{x + 6} = 32$

Step 1

Rewrite $8$ as $2^{3}$ .

$2^{3} \cdot 2^{x + 6} = 32$

Step 2

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

$2^{3 + x + 6} = 32$

Step 3

Add $3$ and $6$ .

$2^{x + 9} = 32$

Step 4

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

$2^{x + 9} = 2^{5}$

Step 5

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

$x + 9 = 5$

Step 6

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

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Step 6.1

Subtract $9$ from both sides of the equation.

$x = 5 - 9$

Step 6.2

Subtract $9$ from $5$ .

$x = - 4$