Question

which expression is equivalent to $\frac{11^{30}}{11^{6}}$?
$11^{5}$
$(11^{6})^{4}$
$(11^{1})^{4}$
$\frac{1}{11^{5}}$

Explanation:

Step1: Apply exponent division rule

When dividing exponents with the same base, subtract the exponents: $a^m \div a^n = a^{m-n}$.
$\frac{11^{30}}{11^6} = 11^{30-6}$

Step2: Calculate the exponent

Subtract the values in the exponent.
$11^{30-6} = 11^{24}$

Step3: Evaluate each option

• Option 1: $11^5

eq 11^{24}$

• Option 2: Use power of a power rule $(a^m)^n = a^{m \times n}$: $(11^6)^4 = 11^{6 \times 4} = 11^{24}$
• Option 3: $(11^1)^4 = 11^{1 \times 4} = 11^4

eq 11^{24}$

• Option 4: $\frac{1}{11^5} = 11^{-5}

eq 11^{24}$

Answer:

$\boldsymbol{(11^6)^4}$