Perform the operation and simplify the answer fully. (1)/(8x^(3))*(5x)/(4) Answer:

Multiply Fractions: Multiply the numerators and denominators separately. We have two fractions to multiply: (1)/(8x^(3)) and (5x)/(4). When multiplying fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together. Calculation: (1 * 5x) / (8x^(3) * 4)Simplify Multiplication: Simplify the multiplication of the numerators and denominators. The numerator is simply 1 * 5x, which is 5x. The denominator is 8x^(3) * 4, which is 32x^(3). Calculation: 5x / 32x^(3)Cancel Common Factors: Simplify the fraction by canceling out common factors. We can cancel out an x from the numerator and denominator because x/x = 1. Calculation: (5x / x) / (32x^(3) / x) = 5 / 32x^(2)Check Further Simplification: Check for any further simplification. The fraction 5 / 32x^(2) is already in its simplest form. There are no common factors left to cancel out, and the numerator and denominator are both in their simplest terms.

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Q. Perform the operation and simplify the answer fully.

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\frac{1}{8 x^{3}} \cdot \frac{5 x}{4}

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Answer:

Multiply Fractions: Multiply the numerators and denominators separately. $\newline$ We have two fractions to multiply: $(\frac{1}{8x^{3}})$ and $(\frac{5x}{4})$ . When multiplying fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together. $\newline$ Calculation: $(\frac{1 \times 5x}{8x^{3} \times 4})$
Simplify Multiplication: Simplify the multiplication of the numerators and denominators. $\newline$ The numerator is simply $1 \times 5x$ , which is $5x$ . The denominator is $8x^{3} \times 4$ , which is $32x^{3}$ . $\newline$ Calculation: $\frac{5x}{32x^{3}}$
Cancel Common Factors: Simplify the fraction by canceling out common factors. $\newline$ We can cancel out an $x$ from the numerator and denominator because $x/x = 1$ . $\newline$ Calculation: $(5x / x) / (32x^{3} / x) = 5 / 32x^{2}$
Check Further Simplification: Check for any further simplification. $\newline$ The fraction $\frac{5}{32x^{2}}$ is already in its simplest form. There are no common factors left to cancel out, and the numerator and denominator are both in their simplest terms.