Question

Use the definitions of exponents to show that each statement is true.

(0.72) to the 7th power > (-7.2) to the 7th power

Answer 1

The given statement is true.

Explanation:

We are asked whether the following statement is true or not:

(0.72) to the 7th power > (-7.2) to the 7th power

This statement is true since the value of
`(0.72)^7=0.10030613`

Also the value of the exponent
`(-7.2)^7` will be negative as odd power of a negative number is always negative.

Also
`(-7.2)^7=-1.003061.3004288`

and we know that any positive number is always greater than negative number.

Hence,
`(0.72)^7>(-7.2)^7`

Hence, the following statement is true.

Answer 2

Answer: The answer is FALSE.

Step-by-step explanation: We are given to check the correctness of the inequality below using the definitions of exponents.

`(0.72)^(7)>(-7.2)^7.`

We will be using the rule of exponents as given below

`(a^x)/(a^y)=a^(x-y),\\\\ a^0=1.`

Let us start as follows:

`((0.72)^7)/((-7.2)^7)\\\\\\=((0.72)^7)/(((-10)* 0.72)^7)\\\\\\=((0.72)^7)/((-10)^7* (1.72)^7)\\\\\\=0.72^(7-7)* (-10^(-7))\\\\\\=1* (-0.0000001)\\\\=-0.0000001<1`

Therefore,

`(0.72)^(7)<(-7.2)^7.`

Thus, the given statement is false.