Question

6
find the missing exponent.
$\frac{5^{11}}{5^{?}} = 5^{4}$
exponent only in the answer box

Explanation:

Step1: Recall exponent division rule

For $a^m \div a^n = a^{m-n}$, or $\frac{a^m}{a^n}=a^{m-n}$

Step2: Let missing exponent be $x$

Set up equation: $\frac{5^{11}}{5^{x}} = 5^{4}$

Step3: Apply exponent rule to left side

$5^{11-x} = 5^{4}$

Step4: Equate exponents (same base)

$11 - x = 4$

Step5: Solve for $x$

$x = 11 - 4 = 7$

Answer:

7