Chapter 6.1, Problem 35E

To determine

To correct:The error in the expression $2^4\cdot 2^5={(2\cdot 2)}^{4+5}=4^9$

Answer to Problem 35E

The correct expression is $2^4\cdot 2^5={(2)}^{4+5}=2^9$

Explanation of Solution

Given information:The incorrect expression

  $2^4\cdot 2^5={(2\cdot 2)}^{4+5}=4^9$

Calculation:The product rule of exponents is given as,

  $a^x\cdot a^y=a^{x+y}$ , for any arbitrary a, x and y

The error in the expression $2^4\cdot 2^5={(2\cdot 2)}^{4+5}=4^9$ is in the 2^nd step where it is written $2^4\cdot 2^5={(2\cdot 2)}^{4+5}$ instead of $2^4\cdot 2^5=2^{4+5}$ .

Thus, the correct solution will be,

  $\begin{array}{l}{2}^4\cdot 2^5\\ =2\\ =2^9\end{array}$