Question

Divide. Assume that all variables in the denominator are nonzero.

Answer 1

Answer:

4$a^{5}$

Step-by-step explanation:

$\frac{64}{16}$ = 4

When the bases are the same and you are dividing you subtract the exponents.  It is easier to see why when you write the problem out in expanded form.

$\frac{aaaaaabbbbbbb}{abbbbbbb}$  If you cross out all of the a's on top with the a's on the bottom, you are left with only 1 a (6-1 = 5)  If you do not see an exponent, it is understood to be 1.  All of the b's on the top and bottom cross out. (7-7 = 0)  Anything to the zero power = 1.

Answer 2

Answer:

4$a^{5}$

Step-by-step explanation:

The easiest way to start this solving is simplifying the numbers:

start by dividing 64 by 16. This gets you 4.

Then simplify the variables. Let's start with a:

to do this, we will start by moving all the a's to the same line so we can multiply them

multiplying like variables means that you are actually just adding their exponents

when moving a variable up or down on the fraction, the exponent will flip signs (positive to negative, or negative to positive)

in this case, we have $a^{6}$ in the numerator and $a^{1}$, so it would be easiest to move   $a^{1}$ above so that it the equation will become $\frac{4a^{6}a^{-1}b^{7} }{b^{7} }$

now we can subtract 1 from 6 and get  $\frac{4a^{5}b^{7} }{b^{7} }$

Now let's work on simplifying b:

both the numerator and denominator have $b^{7}$ in it

so if we move the b denominator up, the numerator ends up as     ${4a^{5}b^{7}b^{-7} }$

which makes both b's cancel out, making your final answer 4$a^{5}$