Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^-14 with positive exponents only.

Answer 1

To simplify the expression \( \frac{3^{-17}}{8^{-14}} \) and generate an equivalent expression with only positive exponents, we need to use the property of negative integer exponents which states that \( a^{-n} = \frac{1}{a^n} \).

1. Rewrite the negative exponents as positive: \[ \frac{3^{-17}}{8^{-14}} = \frac{1}{3^{17}} \cdot \frac{1}{8^{-14}} \] Since \( 8^{-14} \) appears in the denominator, we can express it with a positive exponent by moving it to the numerator: \[ \frac{1}{3^{17}} \cdot 8^{14} \]

2. Combine the terms: \[ = \frac{8^{14}}{3^{17}} \]

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