Pregunta
Simplify, answerwrite with positive exponents: \( \frac{-8 a^{5} b^{9} c}{2 a^{3} b^{8} c^{-3}} \)
Ask by Pollard Ryan. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\[
-4a^{2}bc^{4}
\]
Solución
To simplify the expression \( \frac{-8 a^{5} b^{9} c}{2 a^{3} b^{8} c^{-3}} \) and write it with positive exponents, follow these steps:
1. **Simplify the coefficients:**
\[
\frac{-8}{2} = -4
\]
2. **Simplify the variables by subtracting the exponents (since you're dividing):**
- For \( a \):
\[
a^{5} \div a^{3} = a^{5-3} = a^{2}
\]
- For \( b \):
\[
b^{9} \div b^{8} = b^{9-8} = b^{1} = b
\]
- For \( c \):
\[
c \div c^{-3} = c^{1-(-3)} = c^{4}
\]
3. **Combine all simplified parts:**
\[
-4 \cdot a^{2} \cdot b \cdot c^{4} = -4a^2bc^4
\]
**Final Answer:**
\[
-4a^{2}bc^{4}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To simplify \( \frac{-8 a^{5} b^{9} c}{2 a^{3} b^{8} c^{-3}} \), start by dividing the coefficients and applying the properties of exponents. 1. Divide the coefficients: \( \frac{-8}{2} = -4 \). 2. For \( a^{5} \div a^{3} \), use the rule \( a^{m} \div a^{n} = a^{m-n} \): \[ a^{5-3} = a^{2}. \] 3. For \( b^{9} \div b^{8} \): \[ b^{9-8} = b^{1} = b. \] 4. For \( c \div c^{-3} \), remember that dividing by a negative exponent is the same as multiplying by the positive exponent: \[ c \div c^{-3} = c^{1 - (-3)} = c^{4}. \] Putting it all together: \[ -4 a^{2} b c^{4}. \] Thus, the simplified expression with positive exponents is: \[ \boxed{-4 a^{2} b c^{4}}. \]
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