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 only, we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Applying this property, we rewrite the expression:

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

Thus, the expression with positive exponents only is:

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