Question

Laws of Exponents

Answer 1

Answer:

a = 10 and b = 6

Step-by-step explanation:

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

$\frac{7^{2} 7^{8} }{7^{4} }$

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

$\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}$  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

$\frac{^{10} }{7^{4} }$

Now it looks like

$\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}$  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)