just a few questions (simplifying with exponents)

[shortoneinpa]

First, working with exponents
(3x^5)^4
(6x^4)

my answer was
81x^20
1216x^6

the book has
x^4
16

now i realize how this answer was obtained but what i don't understand is why the x goes at the top and the 16 on bottom?

one more...
(2x^2)^3 (2x^5)^-2
(y^4) ( y) the second y should be under the second set

i do not understand how the book got this
2
x^4y^10

this is what i got
the parentheses mean multiply right?
8x^6 4x^-10
y^12 y^-2 so wouldn't you multiply 8x4

this is my answer
32
x^4y^10

please help, i'm stumped

 

[Denis]

Re: just a few questions

You're doing about 50% of your work correctly; but you're not following ALL the rules :shock:

Go here: http://www.purplemath.com/modules/exponent.htm
Study it all and you'll be an expert :wink:

 

[shortoneinpa]

ok that helped a little, but i'm still stumped. it's the 2, i don't understand why the answer is two at the end

 

[Denis]

(2x^2)^3 (2x^5)^-2
(y^4) ( y) the second y should be under the second set

OK: look at numerator: (2x^2)^3 times (2x^5)^-2
Lets concentrate on the 2's: 2^3 times 2^-2 : that's 2^(3 - 2) = 2 ; remember: a^x * a^y = a^(x + y)
So that's why you end up with a single 2.