a) $$ \frac{\left(11^{3}\right)^{6}}{11^{15}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{\left(11^{3}\right)^{6}}{11^{15}}
$$

**Step 1: Apply the Power of a Power Property**

Recall that $$(a^{m})^{n} = a^{m \times n}$$. Apply this to the numerator:

$$
\left(11^{3}\right)^{6} = 11^{3 \times 6} = 11^{18}
$$

**Step 2: Divide the Powers with the Same Base**

Now, you have:

$$
\frac{11^{18}}{11^{15}}
$$

When dividing powers with the same base, subtract the exponents:

$$
11^{18} \div 11^{15} = 11^{18 - 15} = 11^{3}
$$

**Step 3: Calculate the Final Value**

$$
11^{3} = 11 \times 11 \times 11 = 1331
$$

**Final Answer:**

$$
\frac{\left(11^{3}\right)^{6}}{11^{15}} = 11^{3} = 1331
$$
$$ \frac{\left(11^{3}\right)^{6}}{11^{15}} = 11^{3} = 1331 $$

a) \( \frac{\left(11^{3}\right)^{6}}{11^{15}} \)