Question

Apply the Property of Negative Exponents to generate an expression equivalent to 3^−17/8^−14
with positive exponents only.(1 point)
Responses

1/5^3
the fraction with numerator 1 and denominator 5 cubed

5^3
5 cubed

3^17/8^14
the fraction with numerator 3 to the 17th power and denominator 8 to the 14th power

8^14/3^17

Answer 1

To apply the property of negative exponents, recall that \( a^{-n} = \frac{1}{a^n} \). Using this property, we can rewrite the expression \( \frac{3^{-17}}{8^{-14}} \).

Starting with the expression:

\[
\frac{3^{-17}}{8^{-14}}
\]

We can rewrite it as:

\[
\frac{1}{3^{17}} \div \frac{1}{8^{14}} = \frac{1}{3^{17}} \times 8^{14} = \frac{8^{14}}{3^{17}}
\]

Thus, the expression equivalent to \( \frac{3^{-17}}{8^{-14}} \) with positive exponents is:

\[
\frac{8^{14}}{3^{17}}
\]

So the correct response is:

**8^14/3^17** (the fraction with numerator 8 to the 14th power and denominator 3 to the 17th power).