Question
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Tutor-Verified Answer
Answer
\( b^{-3} \)
Solution
1. We start with the expression:
\[
\frac{b^{7}}{b^{10}}
\]
2. Apply the quotient rule for exponents, which states that for any base \(b\) and exponents \(m\) and \(n\):
\[
\frac{b^{m}}{b^{n}} = b^{m-n}
\]
3. Substitute the values \(m = 7\) and \(n = 10\):
\[
\frac{b^{7}}{b^{10}} = b^{7-10}
\]
4. Simplify the exponent:
\[
7 - 10 = -3
\]
5. Write the final simplified expression:
\[
b^{-3}
\]
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Simplify this solution Extra Insights
To simplify \( \frac{b^{7}}{b^{10}} \), you can use the property of exponents that states \( \frac{a^{m}}{a^{n}} = a^{m-n} \). Applying this property, you get: \[ \frac{b^{7}}{b^{10}} = b^{7-10} = b^{-3} \] If you want to express \( b^{-3} \) in a positive exponent form, it can be rewritten as \( \frac{1}{b^{3}} \). Thus, the simplified expression is \( \frac{1}{b^{3}} \).
