Solve for x (7^7)/(7^3)=7^x

$\frac{7^{7}}{7^{3}} = 7^{x}$

Step 1

Rewrite the equation as $7^{x} = \frac{7^{7}}{7^{3}}$ .

$7^{x} = \frac{7^{7}}{7^{3}}$

Step 2

Move $7^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$7^{x} = 7^{7} \cdot 7^{- 3}$

Step 3

Multiply $7^{7}$ by $7^{- 3}$ by adding the exponents.

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

$7^{x} = 7^{7 - 3}$

Subtract $3$ from $7$ .

$7^{x} = 7^{4}$

Step 4

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

$x = 4$