Question
4) Simplify. Express your answer using positive exponent \( \frac{5 c^{3}}{5 c \cdot c^{0}} \)
Ask by Morgan Adkins. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( c^{2} \)
Solution
1. Write the given expression:
\[
\frac{5 c^{3}}{5 c \cdot c^{0}}
\]
2. Simplify \( c^{0} \) to 1, since any number (except 0) raised to the power 0 is 1:
\[
\frac{5 c^{3}}{5 c \cdot 1} = \frac{5 c^{3}}{5 c}
\]
3. Cancel the common factor of 5 in the numerator and denominator:
\[
\frac{c^{3}}{c}
\]
4. Use the quotient rule for exponents (subtract the exponent in the denominator from the exponent in the numerator):
\[
c^{3-1} = c^2
\]
5. The simplified expression is:
\[
c^2
\]
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Simplify this solution Extra Insights
To simplify the expression \( \frac{5 c^{3}}{5 c \cdot c^{0}} \), first, note that \( c^{0} = 1 \), so the denominator simplifies to \( 5c \). This reduces the expression to \( \frac{5 c^{3}}{5 c} \). The 5’s cancel out, leaving us with \( \frac{c^{3}}{c} \). Applying the property of exponents \( \frac{c^{m}}{c^{n}} = c^{m-n} \), we get \( c^{3-1} = c^{2} \). Thus, the simplified expression is \( c^{2} \).
