Question

1.(3a4)3

Answer 1

That's enough. Please stop spamming.

Answer 2

For raising products to a power, you just multiply the power times the power of the factors:

\[(a^bc)^d = a^{bd}c^d\]

Answer 3

so wait i have to distrubite the power of d??

Answer 4

You multiply the power of each of the factors in parens by the power the whole thing is raised to.

Answer 5

Give it a try and I'll check your answer.

Answer 6

ok so 3a^7

Answer 7

Nope. What is the exponent on any number that doesn't have a specific exponent?

Answer 8

well 3 does not have an exponent

Answer 9

It does though, You just don't have to write it. If it doesn't have an explicit exponent there is always an implied exponent of 1.

Answer 10

Also when you did the 'distribution' you appear to have added. You need to multiply.

Answer 11

so 3 exponent is one?

Answer 12

\[3 = 3^1\]

Answer 13

o ok

Answer 14

so it would be 3a^4+^3

Answer 15

no.

Answer 16

Look at this again.

\[(cb^k)^d = c^db^{k\cdot d}\]

Answer 17

This is the same 'form' of problem as the one you are working on. In your problem what number corrisponds to the c in my example?

Answer 18

3

Answer 19

correct.

Answer 20

3^3a^4+^3

Answer 21

So since the 3 has an exponent of 1, when we multiply the exponent by the outer exponent (3) what will the final exponent be?

Correct 3^3

Answer 22

So now for the a. What is the exponent of the a?

Answer 23

4

Answer 24

And we are raising a^4 to the 3rd power, so we need to multiply the exponent on the a by the exponent we are raising it to.

Answer 25

so what is a^(4*3)

Answer 26

so it would be a^12 power?

Answer 27

Correct. So the final answer is..

Answer 28

Simplify 3^3 to 27

Answer 29

ok so it w makes it to 27a^12

Answer 30

Correct.

The take away message being..
If you have a number without an exponent assume the exponent is 1
AND
If you raise a power to a power, multiply the exponents.

Answer 31

Now lets try your other one.

\[(-2x3y)^4\]

Answer 32

ok so it means -6xy^4

Answer 33

\[(-2)^4 = 2^4 = 16\]

Answer 34

and \(3^4 = 81\)