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 rewrite the expression \( \frac{3^{-17}}{8^{-14}} \) with positive exponents only, we can apply the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

1. Apply the property to the numerator and the denominator:

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

2. Dividing by a fraction is the same as multiplying by its reciprocal:

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

3. This can be rewritten as:

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

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

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