Question

compare 8^0 and 8^-2. which is greater? Explain your reasoning.

Answer 1

Hello there!

$8^0$ amd $8^-2$

Let me start with 8^-2

8^-2 = 1/8 * 8

8^-2 = 1/64

which equals to 0.015625 in decimal

8^ 0 =  1

Yep, that's the answer! Easy, isn't? Well you may have been wondering why 8^0 is equal to 1.

I quoted an explanation online that says:    Think of "multiplication" as always including an extra "1" as a multiplier.

So it'd be like

8^ 0

8/8 = 1

Remember: Whenever a number has an exponent 0, the answer MUST be 1.

Thus,

8^0 is greater. As you can see, it is equal to 1, while the other one is equal to 0.01

I'm terrible at explaining stuff. I hope you find this answer somehow helpful :)

Answer 2

Hey there!

$8^0$ $=$ $1$

$8^{-2}$ $=$ $\frac{1}{64}$ $=$ $0.015625$

$8^0$ $>$ $8^{-2}$

The bigger one is (answer) : $8^0$

Reason: Exponents with $Negatives$ are usually decimals/ fractions, which are $UNDERNEATH$   $0$ and usually exponents with $Positives$  are usually $ABOVE$   $0$

Good luck on your assignment and enjoy your day!  

~$LoveYourselfFirst:)$