Respuesta :
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.
[tex](0.72)^{7}>(-7.2)^7.[/tex]
We will be using the rule of exponents as given below
[tex]\dfrac{a^x}{a^y}=a^{x-y},\\\\ a^0=1.[/tex]
Let us start as follows:
[tex]\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<1[/tex]
Therefore,
[tex](0.72)^{7}<(-7.2)^7.[/tex]
Thus, the given statement is false.
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 [tex](0.72)^7=0.10030613[/tex]
Also the value of the exponent [tex](-7.2)^7[/tex] will be negative as odd power of a negative number is always negative.
Also [tex](-7.2)^7=-1.003061.3004288[/tex]
and we know that any positive number is always greater than negative number.
Hence, [tex](0.72)^7>(-7.2)^7[/tex]
Hence, the following statement is true.
