Chapter 4.5, Problem 59E

a.

To determine

To rewrite the left side of the equation using the quotient of powers property.

Answer to Problem 59E

  $5^{m-n}$

Explanation of Solution

Given information: Left side of equation: $\frac{5^m}{5^n}$

Powers property states that if the bases are same, the exponents would be added during multiplication and subtracted during division.

In this case, there is division of $\frac{5^m}{5^n}$

Hence, it would be written as $5^{m-n}$

b.

To determine

To find the pair of integers for which the given equation is true.

Answer to Problem 59E

  $m=2,n=1$

Explanation of Solution

Given information: $\frac{5^m}{5^n}=5$

To find a pair of ‘m’ and ‘n’ for which the difference between them is 1.

Hence, ‘m’ could be 2 and ‘n’ could be 1.

c.

To determine

To find if there are other pairs of integers for which the equation holds true.

Answer to Problem 59E

Yes

Explanation of Solution

Given information: $\frac{5^m}{5^n}=5$

Powers property states that if the bases are same, the exponents would be added during multiplication and subtracted during division.

To find a pair of m and n for which the above equation holds true. This could only be possible if $m=n+1$ .

Hence, there are many pairs for which the value of ‘n’ could be any integer and the value ‘m’ would be $n+1$