Question
14 Simplify. \( \frac{28 c^{10} d^{13}}{24 c^{6} d^{8}} \)
Ask by Moreno Bartlett. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{7c^{4}d^{5}}{6} \).
Solution
Calculate or simplify the expression \( \frac{28c^{10}d^{13}}{24c^{6}d^{8}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{28c^{10}d^{13}}{24c^{6}d^{8}}\)
- step1: Reduce the fraction:
\(\frac{28c^{10-6}d^{13}}{24d^{8}}\)
- step2: Reduce the fraction:
\(\frac{28c^{4}d^{13}}{24d^{8}}\)
- step3: Reduce the fraction:
\(\frac{28c^{4}d^{13-8}}{24}\)
- step4: Reduce the fraction:
\(\frac{28c^{4}d^{5}}{24}\)
- step5: Reduce the fraction:
\(\frac{7c^{4}d^{5}}{6}\)
The simplified form of \( \frac{28c^{10}d^{13}}{24c^{6}d^{8}} \) is \( \frac{7c^{4}d^{5}}{6} \).
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Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{28 c^{10} d^{13}}{24 c^{6} d^{8}} \), we start by simplifying the coefficients and then the variables separately. First, the coefficients \( \frac{28}{24} \) simplifies to \( \frac{7}{6} \) since both can be divided by 4. Next, for the variable \( c \), we apply the rule of exponents: \( c^{10} / c^{6} = c^{10-6} = c^{4} \). For the variable \( d \), we again apply the exponent rule: \( d^{13} / d^{8} = d^{13-8} = d^{5} \). Putting it all together, we get: \[ \frac{7}{6} c^4 d^5 \] So, the simplified expression is: \(\frac{7 c^{4} d^{5}}{6}\).
