Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3 rasied to the power of −178/−14 with positive exponents only.(1 point) 3 rasied to the power of −178/−14=

Answer 1

To simplify \( 3^{-\frac{178}{-14}} \) using the property of negative integer exponents, we first simplify the exponent \(-\frac{178}{-14}\).

1. Simplifying the fraction:
\[
-\frac{178}{-14} = \frac{178}{14}
\]

2. Next, we can simplify \(\frac{178}{14}\):
- \(178\) and \(14\) can both be simplified by \(2\):
\[
\frac{178 \div 2}{14 \div 2} = \frac{89}{7}
\]

3. Now we rewrite the expression with the positive exponent:
\[
3^{-\frac{178}{-14}} = 3^{\frac{89}{7}}
\]

Thus, the expression equivalent to \( 3^{-\frac{178}{-14}} \) with positive exponents only is:

\[
3^{\frac{89}{7}}
\]