Solve for n 5^n=5^11*5^3

$5^{n} = 5^{11} \cdot 5^{3}$

Step 1

Multiply $5^{11}$ by $5^{3}$ by adding the exponents.

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

$5^{n} = 5^{11 + 3}$

Add $11$ and $3$ .

$5^{n} = 5^{14}$

Step 2

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

$n = 14$