Algebra Examples

$5^{x} = 5^{3} \cdot 5^{8}$

Step 1

Multiply $5^{3}$ by $5^{8}$ 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.

$5^{x} = 5^{3 + 8}$

Step 1.2

Add $3$ and $8$ .

$5^{x} = 5^{11}$

Step 2

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

$x = 11$