Chapter 7.2, Problem 7LC

To determine

To Explain: The error in the equation $4a^{\frac{1}{2}}\cdot 3a^{\frac{1}{5}}=7a^{\frac{1}{7}}$ .

Answer to Problem 7LC

The required correct answer is $12a^{\frac{7}{10}}$ .

Explanation of Solution

Given information:

  $4a^{\frac{1}{2}}\cdot 3a^{\frac{1}{5}}=7a^{\frac{1}{7}}$

Calculation:

  $\begin{array}{l}4a^{\frac{1}{2}}\cdot 3a^{\frac{1}{5}}\\ =\left(4\cdot 3\right)\left(a^{\frac{1}{2}}\cdot a^{\frac{1}{5}}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=12a^{\frac{1}{2}+\frac{1}{5}}$

(Multiply the coefficients and add the exponents with same base)

  $=12a^{\frac{7}{10}}$

(Simplify)

Therefore, the correct answer is $12a^{\frac{7}{10}}$ .