Question

Exponent Rules Unit Test
13 of 1513 of 15 Items

Question
Which of the following is equivalent to 35−4 ⋅ 17−9 generated by the Property of Negative Integer Exponents?(1 point)
Responses

1435 ⋅ 917
Start Fraction 1 over 4 superscript 35 baseline times 9 superscript 17 baseline end fraction

354179
Start Fraction 35 superscript 4 baseline over 17 superscript 9 baseline End Fraction

1354 ⋅ 179
Start Fraction 1 over 35 superscript 4 baseline times 17 superscript 9 baseline end fraction

354 ⋅179
35 superscript 4 baseline times 17 superscript 9 baseline

Answer 1

To solve the problem and find the expression equivalent to \( 35^{-4} \cdot 17^{-9} \) using the property of negative integer exponents, we will apply the rule that states \( a^{-n} = \frac{1}{a^n} \).

Starting from \( 35^{-4} \cdot 17^{-9} \):

1. Apply the negative exponent rule:
\[
35^{-4} \cdot 17^{-9} = \frac{1}{35^{4}} \cdot \frac{1}{17^{9}} = \frac{1}{35^{4} \cdot 17^{9}}
\]

Now, we need to check the given responses to see which one matches our result:

1. **Response A**: \( 1435 \cdot 917 \) - Not correct.
2. **Response B**: \( \frac{1}{4^{35} \cdot 9^{17}} \) - Not correct.
3. **Response C**: \( \frac{35^{4}}{17^{9}} \) - Not correct.
4. **Response D**: \( \frac{1}{35^{4} \cdot 17^{9}} \) - This matches our result.
5. **Response E**: \( 35^{4} \cdot 17^{9} \) - Not correct.

The correct response is:

**Response D**: \( \frac{1}{35^{4} \cdot 17^{9}} \)