Multiple Law of exponents

[crappiefisher26]

the original expressions are

(2a to the -3) to the -4

and
(3x to the 2) to the -3

kinda confused on how to work these type out.

 

[Mrspi]

the original expressions are

(2a to the -3) to the -4

and
(3x to the 2) to the -3

kinda confused on how to work these type out.

I'll walk you through the first problem.

(2 a^-3)^-4

This is a product raised to a power, so we need this rule:

(ab)ⁿ = aⁿ bⁿ
When a product is raised to a power, each factor is raised to that power. Apply this rule to your problem:

2^-4 (a^-3)^-4

Next, we have a power raised to a power, so we need another rule:

(a^m)ⁿ = a^m*n
That is, when you raise a power to a power, you multiply the exponents. Apply this rule to your problem:

2^-4 a^(-3)*(-4)

2^-4 a¹²

Finally, we need to deal with the negative exponent on 2^-4. Remember that

a^-n = 1 / aⁿ

Apply this rule:

(1 / 2⁴) * a¹²

(1/16) a¹²
or,

a¹² / 16

Now, the second problem is done in much the same way. See what you can do with it. If you have difficulty, please repost showing all of your steps.

 

[crappiefisher26]

Im sorry on the first problem the last power should have been 4 not -4

 

[jonboy]

Hmm then what do you think the answer would be? Mrspi gave you a magnificent explanation on how to do solve these types of problems (I even learned from that post).