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:

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