Multiply. Simplify your answer. 7p^2q^2/3p * 6pq^2 ______

Write Multiplication Expression: Write down the multiplication of the two fractions. We have the expression 7p^2q^2/3p * 6pq^2. To multiply fractions, we multiply the numerators together and the denominators together.Multiply Numerators and Denominators: Multiply the numerators and the denominators. The numerators are 7p^2q^2 and 6pq^2, and the denominator is 3p. Multiplying the numerators gives us 7 * 6 * p^2 * p * q^2 * q^2. Multiplying the denominator by 1 (since there is no denominator in the second fraction) gives us 3p.Perform Numerator Multiplication: Perform the multiplication of the numerators. 7 * 6 * p^2 * p * q^2 * q^2 = 42p^3q^4.Combine with Denominator: Combine the multiplication of the numerators with the denominator. We have 42p^3q^4 over 3p.Simplify Fraction: Simplify the fraction by canceling common factors. We can cancel a p from the numerator and the denominator, and we can also divide both the numerator and the denominator by 3. 42p^3q^4 / 3p = (42/3) * (p^3/p) * q^4 = 14p^2q^4.

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Math Problems

Algebra 1

Multiply and divide rational expressions

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Q. Multiply. Simplify your answer.

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\frac{7p^2q^2}{3p} \times 6pq^2

Write Multiplication Expression: Write down the multiplication of the two fractions. We have the expression $\frac{7p^2q^2}{3p} \times 6pq^2$ . To multiply fractions, we multiply the numerators together and the denominators together.
Multiply Numerators and Denominators: Multiply the numerators and the denominators. $\newline$ The numerators are $7p^2q^2$ and $6pq^2$ , and the denominator is $3p$ . Multiplying the numerators gives us $7 \times 6 \times p^2 \times p \times q^2 \times q^2$ . Multiplying the denominator by $1$ (since there is no denominator in the second fraction) gives us $3p$ .
Perform Numerator Multiplication: Perform the multiplication of the numerators. $7 \times 6 \times p^2 \times p \times q^2 \times q^2 = 42p^3q^4$ .
Combine with Denominator: Combine the multiplication of the numerators with the denominator. $\newline$ We have $\frac{42p^3q^4}{3p}$ .
Simplify Fraction: Simplify the fraction by canceling common factors. $\newline$ We can cancel a $p$ from the numerator and the denominator, and we can also divide both the numerator and the denominator by $3$ . $\newline$ $\frac{42p^3q^4}{3p} = \left(\frac{42}{3}\right) \times \left(\frac{p^3}{p}\right) \times q^4 = 14p^2q^4$ .