Algebra Examples

$2^{5} \cdot 2^{x} = 256$

Step 1

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

$2^{5 + x} = 256$

Step 2

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

$2^{5 + x} = 2^{8}$

Step 3

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

$5 + x = 8$

Step 4

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

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Step 4.1

Subtract $5$ from both sides of the equation.

$x = 8 - 5$

Step 4.2

Subtract $5$ from $8$ .

$x = 3$