Perform the operation and simplify the answer fully. (9)/(7x^(3))*(3)/(2x^(3)) Answer:

Identify Given Expression: Identify the given expression and the operation to be performed. The expression is (9)/(7x^(3))*(3)/(2x^(3)), and we need to multiply the two fractions.Multiply Numerators and Denominators: Multiply the numerators and the denominators separately. (9 * 3) / (7x^(3) * 2x^(3))Calculate Product: Calculate the product of the numerators. 9 * 3 = 27Calculate Product of Denominators: Calculate the product of the denominators using the property of exponents (x^(a) * x^(b) = x^(a+b)). 7 * 2 = 14 and x^(3) * x^(3) = x^(3+3) = x^(6)Combine Results: Combine the results of the numerator and denominator multiplication. 27 / (14x^(6))Check for Further Simplification: Check if the fraction can be simplified further. Since 27 and 14 have no common factors other than 1, and the variable part is already simplified, the fraction is in its simplest form.

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Perform the operation and simplify the answer fully.

\newline

\frac{9}{7 x^{3}} \cdot \frac{3}{2 x^{3}}

\newline

Answer:

Identify Given Expression: Identify the given expression and the operation to be performed. $\newline$ The expression is $(9)/(7x^{3})$ $(3)/(2x^{3})$ , and we need to multiply the two fractions.
Multiply Numerators and Denominators: Multiply the numerators and the denominators separately. $\newline$ $(9 \times 3) / (7x^{3} \times 2x^{3})$
Calculate Product: Calculate the product of the numerators. $9 \times 3 = 27$
Calculate Product of Denominators: Calculate the product of the denominators using the property of exponents $x^{a} \times x^{b} = x^{a+b}$ . $7 \times 2 = 14$ and $x^{3} \times x^{3} = x^{3+3} = x^{6}$
Combine Results: Combine the results of the numerator and denominator multiplication. $\frac{27}{14x^{6}}$
Check for Further Simplification: Check if the fraction can be simplified further. $\newline$ Since $27$ and $14$ have no common factors other than $1$ , and the variable part is already simplified, the fraction is in its simplest form.