Question

(2x^2)^4

Answer 1

helo, helpp.?

Answer 2

do you know that the exponent means multiply by itself that many times?

(2x^2)^4 means multiply
(2x^2) by itself 4 times. Like this:
(2x^2)(2x^2)(2x^2)(2x^2)

Answer 3

when you multiply, you can change the order, so you could write it
2*2*2*2 * x^2 * x^2 * x^2 * x^2

Answer 4

or, knowing that x^2 is x*x
2*2*2*2 * x*x* x*x* x*x* x*x

Answer 5

so i multiply the whole number ? and the exponent?

Answer 6

most people would use the short-cut exponent idea to rewrite
x*x* x*x* x*x* x*x

that is x times itself how many times ?

Answer 7

8

Answer 8

so its 16x^8?

Answer 9

and though you could write 2*2*2*2 as 2^4 (using the exponent idea)
most people would just multiply it out and get 16

Answer 10

so i always multiply the exponents?

Answer 11

yes, 16x^8


there is a short cut to doing the problem

\[ \left(2 x^2\right)^4 = 2^4 \cdot \left(x^2\right)^4 \]
we apply the exponent to each factor.

then we use this "rule"
\[ \left(x^a\right)^b= x^{ab} \]
to get
\[ 2^4 \cdot \left(x^2\right)^4 = 2^4 \cdot x^8 = 16 x^8\]

Answer 12

okay so is that a yes ialways multiply the exponents?

Answer 13

you don't multiply exponents. play with the idea a few minutes.

example: x^2 * x^2 means x*x * x*x = x^4
notice the 2+2= 4

or
x^1 * x^3 = x* x*x*x = x^4
1+3 = 4

it's a nice short-cut to remember.

Answer 14

What if i have (81m^8)(4m^6)
I do 81 x 4
and 8 x 6?

Answer 15

you do multiply exponents if you have
\[ \left(x^a\right)^b \]

you can remember this by remembering a simple example. if a is 1 and b is 3:
\[ \left(x^1\right)^3 = x^1 \cdot x^1 \cdot x^1 = x^3 \]
(the 3 means multiply the stuff in the parens by itself 3 times)

Answer 16

or do i add the exponents in that case?

Answer 17

(81m^8)(4m^6)

that means
81 * 4 * m^8 * m^6

so 4*81= 324 is correct
m^8 * m^6
remember that means
x*x*x*x*x*x*x*x
and m^6 means x*x*x*x*x*x
so m^8 * m^6 means
x*x*x*x*x*x*x*x * x*x*x*x*x*x
which, using the exponent short-cut is written x^14

it should make sense we add exponents when you multiply x^8 * x^6 = x^14

Answer 18

ohhh okay i think i got it

Answer 19

if you do the problems by "expanding" the exponents, it becomes more clear what the answer should be. And because it's so much work, you will learn the exponent idea pretty quick (because it's easier)

Answer 20

HOw do i simplify This tho

2^12/2^10

Answer 21

its supposed to be a fraction

Answer 22

I'll do 2^3 / 2^2 as an example
\[ \frac{2^3}{2^2} = \frac{2\cdot 2 \cdot 2}{2\cdot 2} =2 \]

because 2/2 = 1, and we can simplify two 2/2 leaving just one last 2

if we look at the exponents, 3 -2 = 1
notice we subtracted exponents (that is the fast way)

Answer 23

2^12 will have 2*2*2*2*2*2*2*2*2*2*2*2
divided by 2*2*2*2*2*2*2*2*2*2
(if I counted correctly)
the 10 2's in the bottom will "cancel" 10 2's up top, leaving two 2's left over

or using the exponent idea: 2^(12-10) = 2^2 =2*2 = 4

Answer 24

confusing ?