Question

Laws of Exponents

Instruction Active
Simplifying Products and Quotients of Powers
7² 78
74
a=
=
79
75
-
75
b=

Answer 1

a = 10 and b = 6

Explanation:

I am having a little trouble reading the numbers, but I think that I see

`(7^(2) 7^(8) )/(7^(4) )`

If we wrote this in expanded form, it would look like:

`(7x7x7x7x7x7x7x7x7x7)/(7x7x7x7)` How many 7s are on the top? 10 That is the answer to a. The product of powers principle tells us that if we are multiplying powers with the same bases we add the exponents 2 + 8 = 10

`(^(10) )/(7^(4) )`

Now it looks like

`(7x7x7x7x7x7x7x7x7x7)/(7x7x7x7)` if we cross the 7's out in the top and the bottom, we are left with 6 7's on the top. That is the answer to b.

The quotient of powers principle tells us that if we are dividing powers with the same bases, we can subtract the exponents (10 -4 = 6)