Chapter 4.1, Problem 57IP

To determine

Find the true statement replace with $<,>or=$ .

Answer to Problem 57IP

The true statement value is ${\left(-4\right)}^6>{\left(-4\right)}^7$ .

Explanation of Solution

Given information: Given statement is ${\left(-4\right)}^6\ast {\left(-4\right)}^7$

Calculation:

  $\begin{array}{l}{\left(-4\right)}^6\ast {\left(-4\right)}^7\\ {\left(-4\right)}^6=\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\text{ multiply}\\ =\mathrm{16.16.16}\\ =4,096\\ {\left(-4\right)}^7=\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\left(-4\right)\text{ multiply}\\ =\mathrm{16.16.16.}\left(-4\right)\\ =-16,384\\ \text{Then the true statement value is}\\ {\left(-4\right)}^6>{\left(-4\right)}^7\end{array}$

Thus, the true statement value is ${\left(-4\right)}^6>{\left(-4\right)}^7$ .