Question
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14
3
−
17
8
−
14
with positive exponents only.(1 point)
3−178−14=
3
−
17
8
−
14
=
3
−
17
8
−
14
with positive exponents only.(1 point)
3−178−14=
3
−
17
8
−
14
=
Answers
Answered by
GPT-4o mini
To rewrite the expression \( 3^{-17} 8^{-14} \) with positive exponents, we can apply the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
Applying this property:
1. For \( 3^{-17} \):
\[
3^{-17} = \frac{1}{3^{17}}
\]
2. For \( 8^{-14} \):
\[
8^{-14} = \frac{1}{8^{14}}
\]
Now, substituting these into the original expression gives:
\[
3^{-17} 8^{-14} = \left( \frac{1}{3^{17}} \right) \left( \frac{1}{8^{14}} \right)
\]
Next, we multiply the two fractions together:
\[
= \frac{1}{3^{17} \cdot 8^{14}}
\]
Thus, the expression \( 3^{-17} 8^{-14} \) rewritten with positive exponents only is:
\[
\frac{1}{3^{17} \cdot 8^{14}}
\]
Applying this property:
1. For \( 3^{-17} \):
\[
3^{-17} = \frac{1}{3^{17}}
\]
2. For \( 8^{-14} \):
\[
8^{-14} = \frac{1}{8^{14}}
\]
Now, substituting these into the original expression gives:
\[
3^{-17} 8^{-14} = \left( \frac{1}{3^{17}} \right) \left( \frac{1}{8^{14}} \right)
\]
Next, we multiply the two fractions together:
\[
= \frac{1}{3^{17} \cdot 8^{14}}
\]
Thus, the expression \( 3^{-17} 8^{-14} \) rewritten with positive exponents only is:
\[
\frac{1}{3^{17} \cdot 8^{14}}
\]
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