Chapter 7.3, Problem 70PPS

To determine

To simplify the given expression.

Answer to Problem 70PPS

  $c^{\frac{1}{3}}\cdot c^{\frac{2}{3}}=c$

Explanation of Solution

Given:

Expression: $c^{\frac{1}{3}}\cdot c^{\frac{2}{3}}$

Formula used:

  $x^a\cdot x^b=x^{a+b}$

Calculation:

Consider the given expression,

  $\Rightarrow c^{\frac{1}{3}}\cdot c^{\frac{2}{3}}$

Substituting the above formula in the given expression,

  $\begin{array}{l}\Rightarrow c^{\frac{1}{3}}\cdot c^{\frac{2}{3}}\\ \Rightarrow c^{\frac{1}{3}+\frac{2}{3}}\\ \Rightarrow c^{\frac{1+2}{3}}\\ \Rightarrow c^{\frac{3}{3}}\\ \Rightarrow c^1\\ \Rightarrow c\end{array}$

Conclusion:

Therefore, the simplified form of the equation is c.