Pregunta
11 Simplify. \( \frac{14 a^{3} b^{4}}{4 a b} \)
Ask by Luna Stanley. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The simplified expression is \( \frac{7a^{2}b^{3}}{2} \).
Solución
1. Write the original expression:
\[
\frac{14a^{3}b^{4}}{4ab}
\]
2. Simplify the coefficients by dividing \(14\) by \(4\):
\[
\frac{14}{4} = \frac{7}{2}
\]
3. Simplify the \(a\) terms by subtracting the exponents:
\[
a^{3} \div a = a^{3-1} = a^2
\]
4. Simplify the \(b\) terms by subtracting the exponents:
\[
b^{4} \div b = b^{4-1} = b^3
\]
5. Combine the simplified components:
\[
\frac{7a^2b^3}{2}
\]
Thus, the simplified expression is:
\[
\frac{7a^2b^3}{2}
\]
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Simplifique esta solución The Deep Dive
First, let's break it down! You can simplify the expression by dividing the coefficients and the variables separately. The coefficients \(14\) and \(4\) can be simplified to \(3.5\) (or simply divide them as \(14 \div 4 = 3.5\)), and for the variables, you subtract the exponents. So for \(a^3\) divided by \(a\) (or \(a^1\)), you get \(a^{3-1} = a^{2}\). And for \(b^4\) divided by \(b\) (or \(b^1\)), it becomes \(b^{4-1} = b^{3}\). Putting it all together, the simplified form is: \[ \frac{14 a^{3} b^{4}}{4 a b} = 3.5 a^{2} b^{3} \] But if you're looking for whole numbers, you can multiply everything by \(2\) to clear the fraction, yielding: \[ 7 a^{2} b^{3} \]
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