QuestionJuly 15, 2025

Simplify the expression below: (24x^9)/(48x^5) (x^4)/(2) (5x)/(2) 2x^4 2x^7

Simplify the expression below: (24x^9)/(48x^5) (x^4)/(2) (5x)/(2) 2x^4 2x^7
Simplify the expression below:
(24x^9)/(48x^5)
(x^4)/(2)
(5x)/(2)
2x^4
2x^7

Solution
4.2(173 votes)

Answer

\frac{5}{4}x^{8} + \frac{5}{4}x^{5} + x^{11} Explanation 1. Simplify the first fraction Divide coefficients and subtract exponents: \frac{24}{48} = \frac{1}{2} and x^{9-5} = x^4. Result: \frac{1}{2}x^4. 2. Multiply simplified fraction by remaining terms Multiply \frac{1}{2}x^4 by each term: - \frac{x^4}{2}: \frac{1}{2}x^4 \cdot \frac{x^4}{2} = \frac{1}{4}x^{8}. - \frac{5x}{2}: \frac{1}{2}x^4 \cdot \frac{5x}{2} = \frac{5}{4}x^{5}. - 2x^4: \frac{1}{2}x^4 \cdot 2x^4 = x^{8}. - 2x^7: \frac{1}{2}x^4 \cdot 2x^7 = x^{11}. 3. Combine all results Add all terms: \frac{1}{4}x^{8} + \frac{5}{4}x^{5} + x^{8} + x^{11}. 4. Simplify expression Combine like terms: x^{8} + \frac{1}{4}x^{8} = \frac{5}{4}x^{8}.

Explanation

1. Simplify the first fraction<br /> Divide coefficients and subtract exponents: $\frac{24}{48} = \frac{1}{2}$ and $x^{9-5} = x^4$. Result: $\frac{1}{2}x^4$.<br /><br />2. Multiply simplified fraction by remaining terms<br /> Multiply $\frac{1}{2}x^4$ by each term:<br />- $\frac{x^4}{2}$: $\frac{1}{2}x^4 \cdot \frac{x^4}{2} = \frac{1}{4}x^{8}$.<br />- $\frac{5x}{2}$: $\frac{1}{2}x^4 \cdot \frac{5x}{2} = \frac{5}{4}x^{5}$.<br />- $2x^4$: $\frac{1}{2}x^4 \cdot 2x^4 = x^{8}$.<br />- $2x^7$: $\frac{1}{2}x^4 \cdot 2x^7 = x^{11}$.<br /><br />3. Combine all results<br /> Add all terms: $\frac{1}{4}x^{8} + \frac{5}{4}x^{5} + x^{8} + x^{11}$.<br /><br />4. Simplify expression<br /> Combine like terms: $x^{8} + \frac{1}{4}x^{8} = \frac{5}{4}x^{8}$.
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