What are the rules for positive integral exponent?

Answer 1

There are 5 laws:

Product Law:

This is when the same bases are being multiplied

ex. 83 X 82 this is the same as 8x8x8 8x8

when the same bases are being multiplied you just add the exponents so the answer would be 85

Quotient Law:

This is when the same bases are being divided.

ex. 83 divided by 82 in other words 8x8x8 divided by 8x8

when the same bases are being divided you just subtract the exponents so the answer would be 81

Power of product law:

here is an example : (8x3)2 in this problem all you have to do is apply the exponent to each number in side the bracket or multiply the exponent to each exponent inside the brackets, if there is no exponent you assume there is a 1 so you would do 8 1x2 and 3 1x2 and the answer would be 82x32

Power of quotient law:

this is the same as the one above, you basically just multiply the exponent to the numbers inside the brackets.

So if it was (8 divided by 3)4 you would assume there is an exponent 1 for both the numbers and multiply by four. 8 1x4 divided by 31x4 = 84 divided by 34

Power of a power law:

What do you do if there is already an exponent inside the brackets?

ex. (84)5 you would do the same thing. You multiply the exponents!

if you put the question in standard form it is 8x8x8x8 repeated five times

8x8x8x8 8x8x8x8 8x8x8x8 8x8x8x8 8x8x8x8 how many 8s are there? 20

how do you solve in a much simpler way? you do 84x5 and get the 820