Chapter 4.9, Problem 11MRE

To determine

To simplify: the given algebraic expression

Answer to Problem 11MRE

The simplified algebraic expression is $\boxed{y^4/5}$

Explanation of Solution

Given information: $\left(\frac{1}{3}{y}^3\right)\left(\frac{3}{5}y\right)$

Concept Involved:

We need to use the exponent rule to rewrite the given expression. When multiplying fraction we need to multiply numerator with numerator and denominator with denominator.

Formula Used:

  $a^m\times a^n=a^{m+n}$

Calculation:

Multiply fractions

  $\frac{1}{3}\cdot \frac{3}{5}\cdot y^3\cdot y=\frac{1}{5}\cdot y^3\cdot y$

Use the exponent rule $a^m\times a^n=a^{m+n}$ to simplify $y^3\cdot y$

  $\frac{1}{5}\cdot y^{3+1}=\frac{y^4}{5}$

Conclusion:

The algebraic expression $\left(\frac{1}{3}{y}^3\right)\left(\frac{3}{5}y\right)$ is simplified to give $\boxed{y^4/5}$