Solve for $$ x $$ $$ \frac{7^{7}}{7^{3}}=7^{x} $$ $$ x=\square $$

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UpStudy AI · Accepted Answer

1. We start with the equation:
   $$
   \frac{7^{7}}{7^{3}} = 7^{x}
   $$

2. Using the exponent rule:
   $$
   \frac{a^{m}}{a^{n}} = a^{m-n}
   $$
   we simplify the left-hand side:
   $$
   \frac{7^{7}}{7^{3}} = 7^{7-3} = 7^{4}
   $$

3. Equate the exponents on both sides since the bases are the same:
   $$
   7^{4} = 7^{x}
   $$
   This implies:
   $$
   x = 4
   $$

$$ x=\boxed{4} $$
$$ x=4 $$

Solve for \( x \) \( \frac{7^{7}}{7^{3}}=7^{x} \) \( x=\square \)

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