Perform the operation and simplify the answer fully. (1)/(6x^(3))*(4)/(5x^(2)) Answer:

Identify Given Expression: Identify the given expression and the operation to be performed. The expression is (1)/(6x^(3))*(4)/(5x^(2)), and we need to multiply the two fractions.Multiply Numerators and Denominators: Multiply the numerators and the denominators of the fractions separately. (1 * 4) / (6x^(3) * 5x^(2)) = 4 / (30x^(3 + 2))Simplify Exponents in Denominator: Simplify the multiplication of the exponents in the denominator. When multiplying like bases, we add the exponents. 30x^(3 + 2) = 30x^(5)Simplify Fraction: Simplify the fraction by reducing it to its simplest form. 4 / (30x^(5)) can be simplified by dividing both the numerator and the denominator by 2. (4/2) / (30x^(5)/2) = 2 / (15x^(5))Check for Full Simplification: Check if the fraction is fully simplified. Since there are no common factors between 2 and 15x^(5), the fraction is fully simplified.

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Q. Perform the operation and simplify the answer fully.

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\frac{1}{6 x^{3}} \cdot \frac{4}{5 x^{2}}

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Answer:

Identify Given Expression: Identify the given expression and the operation to be performed. $\newline$ The expression is $(\frac{1}{6x^{3}})\cdot(\frac{4}{5x^{2}})$ , and we need to multiply the two fractions.
Multiply Numerators and Denominators: Multiply the numerators and the denominators of the fractions separately. $\newline$ $(1 \times 4) / (6x^{3} \times 5x^{2}) = 4 / (30x^{3 + 2})$
Simplify Exponents in Denominator: Simplify the multiplication of the exponents in the denominator. $\newline$ When multiplying like bases, we add the exponents. $\newline$ $30x^{(3 + 2)} = 30x^{5}$
Simplify Fraction: Simplify the fraction by reducing it to its simplest form. $\frac{4}{30x^{5}}$ can be simplified by dividing both the numerator and the denominator by $2$ . $\left(\frac{4}{2}\right) / \left(\frac{30x^{5}}{2}\right) = \frac{2}{15x^{5}}$
Check for Full Simplification: Check if the fraction is fully simplified. $\newline$ Since there are no common factors between $2$ and $15x^{5}$ , the fraction is fully simplified.