Solve for a (5^9)/(5^3)=5^a

$\frac{5^{9}}{5^{3}} = 5^{a}$

Step 1

Rewrite the equation as $5^{a} = \frac{5^{9}}{5^{3}}$ .

$5^{a} = \frac{5^{9}}{5^{3}}$

Step 2

Move $5^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5^{a} = 5^{9} \cdot 5^{- 3}$

Step 3

Multiply $5^{9}$ by $5^{- 3}$ by adding the exponents.

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

$5^{a} = 5^{9 - 3}$

Subtract $3$ from $9$ .

$5^{a} = 5^{6}$

Step 4

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

$a = 6$