Question

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

Answer 1

Answer:

The given statement is true.

Step-by-step 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

$\dfrac{a^x}{a^y}=a^{x-y},\\\\ a^0=1.$

Let us start as follows:

$\dfrac{(0.72)^7}{(-7.2)^7}\\\\\\=\dfrac{(0.72)^7}{((-10)\times 0.72)^7}\\\\\\=\dfrac{(0.72)^7}{(-10)^7\times (1.72)^7}\\\\\\=0.72^{7-7}\times (-10^{-7})\\\\\\=1\times (-0.0000001)\\\\=-0.0000001$

Therefore,

$(0.72)^{7}$

Thus, the given statement is false.