Pregunta
implify: \( \frac{32 a b c}{64 a c} \times \frac{8 b c}{4 b^{2}} \)
Ask by Munoz Haynes. in South Africa
Feb 19,2025
Solución de inteligencia artificial de Upstudy
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The simplified form of the expression is \( c \).
Solución
Calculate or simplify the expression \( \frac{32a*b*c}{64a*c} \times \frac{8b*c}{4b^{2}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{32abc}{64ac}\times \frac{8bc}{4b^{2}}\)
- step1: Divide the terms:
\(\frac{b}{2}\times \frac{8bc}{4b^{2}}\)
- step2: Divide the terms:
\(\frac{b}{2}\times \frac{2c}{b}\)
- step3: Reduce the fraction:
\(1\times c\)
- step4: Multiply the terms:
\(c\)
The simplified form of the expression \( \frac{32 a b c}{64 a c} \times \frac{8 b c}{4 b^{2}} \) is \( c \).
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Simplifique esta solución Mind Expander
To simplify the expression, start with the two fractions: \[ \frac{32 a b c}{64 a c} \times \frac{8 b c}{4 b^{2}} \] First, simplify each fraction separately: 1. **For the first fraction:** \[ \frac{32 a b c}{64 a c} = \frac{32 \cancel{a} \cancel{c} b}{64 \cancel{a} \cancel{c}} = \frac{32 b}{64} = \frac{1}{2} b \] 2. **For the second fraction:** \[ \frac{8 b c}{4 b^{2}} = \frac{8 \cancel{b} c}{4 \cancel{b} b} = \frac{8 c}{4 b} = 2 \frac{c}{b} \] Now, multiply the simplified results together: \[ \left(\frac{1}{2} b\right) \times \left(2 \frac{c}{b}\right) = \frac{1}{2} b \cdot 2 \frac{c}{b} = \frac{2bc}{2b} = c \] Thus, the simplified expression is: \[ \boxed{c} \]
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