Question

Think About the Process  Simplify this expression. Assume that b and w are nonzero. Which​ rule(s) for exponents did you​ use?
StartFraction b Superscript 4 Baseline w Superscript 18 Over b Superscript 4 Baseline w Superscript 4 EndFraction
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Part 1
StartFraction b Superscript 4 Baseline w Superscript 18 Over b Superscript 4 Baseline w Superscript 4 EndFraction
equals
  
enter your response here ​(Type your answer using exponential​ notation.)
Part 2
Which​ rule(s) for exponents did you​ use? Select all that apply.
A.
Power of a Product
B.
Dividing Powers with the Same Base
C.
Zero Exponent Property
D.
Power of a Power
E.
Multiplying Powers with the Same Base
F.
Power of a Quotient

Answer 1

To simplify the expression

\[
\frac{b^4 w^{18}}{b^4 w^4},
\]

we will apply the following rules for exponents.

### Part 1: Simplifying the Expression

1. **Dividing Powers with the Same Base:** When dividing powers with the same base, you subtract the exponents. We have \(b^4\) in both the numerator and the denominator:

\[
\frac{b^4}{b^4} = b^{4-4} = b^0 = 1.
\]

So, \(b^4\) cancels out to 1.

2. Now we simplify the \(w\) terms:

\[
\frac{w^{18}}{w^4} = w^{18-4} = w^{14}.
\]

Combining these results, we have:

\[
1 \cdot w^{14} = w^{14}.
\]

So, the simplified expression is:

\[
\boxed{w^{14}}.
\]

### Part 2: Rules Used

In simplifying the expression, the rules for exponents used were:

- **B. Dividing Powers with the Same Base**: This was used for \(b^4\) and \(w^{18}/w^4\).

Therefore, the correct answer is:

- **B. Dividing Powers with the Same Base**.