Perform the operation and simplify the answer fully. (8x^(3))/(5)*(2)/(3x^(2)) Answer:

Identify Operation: Write down the expression and identify the operation to be performed. We have the expression (8x^(3))/(5) * (2)/(3x^(2)). The operation to be performed is multiplication of two fractions.Multiply Numerators and Denominators: Multiply the numerators and denominators separately. When multiplying fractions, we multiply the numerators together and the denominators together. So, we have: Numerator: 8x^(3) * 2 Denominator: 5 * 3x^(2)Perform Numerator Multiplication: Perform the multiplication of the numerators. 8x^(3) * 2 = 16x^(3)Perform Denominator Multiplication: Perform the multiplication of the denominators. 5 * 3x^(2) = 15x^(2)Write New Fraction: Write the new fraction after multiplication. The new fraction after multiplying the numerators and denominators is: (16x^(3))/(15x^(2))Simplify Fraction: Simplify the fraction by canceling common factors. We can cancel x^(2) from the numerator and the denominator because it is a common factor. (16x^(3))/(15x^(2)) = (16/15)x^(3-2) = (16/15)x^(1)Write Final Expression: Write the final simplified expression. The final simplified expression is (16/15)x.

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Perform the operation and simplify the answer fully.

(8x^(3))/(5)*(2)/(3x^(2))
Answer:

Perform the operation and simplify the answer fully. $\newline$ $\frac{8 x^{3}}{5} \cdot \frac{2}{3 x^{2}}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Perform the operation and simplify the answer fully.

\newline

\frac{8 x^{3}}{5} \cdot \frac{2}{3 x^{2}}

\newline

Answer:

Identify Operation: Write down the expression and identify the operation to be performed. $\newline$ We have the expression $(\frac{8x^{3}}{5}) \times (\frac{2}{3x^{2}})$ . The operation to be performed is multiplication of two fractions.
Multiply Numerators and Denominators: Multiply the numerators and denominators separately. $\newline$ When multiplying fractions, we multiply the numerators together and the denominators together. So, we have: $\newline$ Numerator: $8x^{3} \times 2$ $\newline$ Denominator: $5 \times 3x^{2}$
Perform Numerator Multiplication: Perform the multiplication of the numerators. $8x^{3} \times 2 = 16x^{3}$
Perform Denominator Multiplication: Perform the multiplication of the denominators. $5 \times 3x^{2} = 15x^{2}$
Write New Fraction: Write the new fraction after multiplication. $\newline$ The new fraction after multiplying the numerators and denominators is: $\newline$ $(\frac{16x^{3}}{15x^{2}})$
Simplify Fraction: Simplify the fraction by canceling common factors. $\newline$ We can cancel $x^{2}$ from the numerator and the denominator because it is a common factor. $\newline$ $\frac{16x^{3}}{15x^{2}}$ = $\frac{16}{15}x^{3-2}$ = $\frac{16}{15}x^{1}$
Write Final Expression: Write the final simplified expression. $\newline$ The final simplified expression is $\frac{16}{15}x$ .