Question

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)%0D%0A3−178−14=%0D%0A3%0D%0A−%0D%0A17%0D%0A8%

Answer 1

To convert the expression \( 3^{-1} 7^{-1} 8^{-1} \) into an equivalent expression with positive exponents only, you can use the property of negative integer exponents, which states that:

\[
a^{-n} = \frac{1}{a^n}
\]

Applying this property to each term in the expression:

1. For \( 3^{-1} \):
\[
3^{-1} = \frac{1}{3^1} = \frac{1}{3}
\]

2. For \( 7^{-1} \):
\[
7^{-1} = \frac{1}{7^1} = \frac{1}{7}
\]

3. For \( 8^{-1} \):
\[
8^{-1} = \frac{1}{8^1} = \frac{1}{8}
\]

Now, substituting these back into the original expression:

\[
3^{-1} 7^{-1} 8^{-1} = \frac{1}{3} \cdot \frac{1}{7} \cdot \frac{1}{8}
\]

This can be combined into a single fraction:

\[
\frac{1}{3 \cdot 7 \cdot 8}
\]

Now calculating the denominator:

\[
3 \cdot 7 = 21 \quad \text{and} \quad 21 \cdot 8 = 168
\]

Thus:

\[
3^{-1} 7^{-1} 8^{-1} = \frac{1}{168}
\]

So, the expression \( 3^{-1} 7^{-1} 8^{-1} \) with positive exponents only is:

\[
\frac{1}{168}
\]