Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14

Question

with positive exponents only.(1 point)
3^−17/8^−14=

Answer 1

To convert the expression \( \frac{3^{-17}}{8^{-14}} \) to one with positive exponents, we apply the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Using this property, we can rewrite the expression:

\[ \frac{3^{-17}}{8^{-14}} = \frac{1}{3^{17}} \cdot 8^{14} \]

This can also be expressed as:

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

Now, we can keep it as \( \frac{8^{14}}{3^{17}} \) which has only positive exponents.

Thus, the final equivalent expression with positive exponents only is:

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