Question

Apply the Properly of Negative Integer Exponents to generate an expression equivalent to 3-¹⁷/8-¹⁴ with positive exponents only. (1 point)

Answer 1

To rewrite the expression \( \frac{3^{-17}}{8^{-14}} \) using only positive exponents, we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

1. Start with the given expression:
\[
\frac{3^{-17}}{8^{-14}}
\]

2. Apply the property of negative exponents:
- Rewrite \( 3^{-17} \) as \( \frac{1}{3^{17}} \)
- Rewrite \( 8^{-14} \) as \( \frac{1}{8^{14}} \)

Thus, the expression becomes:
\[
\frac{1}{3^{17}} \div \frac{1}{8^{14}}
\]

3. Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{3^{17}} \times 8^{14}
\]

4. This can be simplified to:
\[
\frac{8^{14}}{3^{17}}
\]

Now, the expression \( \frac{3^{-17}}{8^{-14}} \) has been rewritten with positive exponents only:
\[
\frac{8^{14}}{3^{17}}
\]