Question

Rewrite this expression in the simplest radical form. (4x^3 y^4)^3/2

Answer 1

Do you cube this, and then find the square root of that? What's the rules here?

Answer 2

\[(a^bc^d)^e=a^{b \times e}c^{d \times e}\]

Answer 3

I know. I just want to know what the power of 3/2 translates too

Answer 4

\[(Aa^bc^d)^e=A^ea^{b \times e}c^{d \times e}\]

Answer 5

Would this be the square root of 4x^9 y^12

Answer 6

?

Answer 7

3/2 translates to cubed then square rooted. but if you use the distributive rule for exponents I gave you you'll get the answer

Answer 8

you can take the square root first then cube it if you'd like. there's no difference

Answer 9

so my answer is correct then, right?

Answer 10

you have to cube the constant as well

Answer 11

its multiple choice the answer i gave was one of them. could it be even more simplified?

Answer 12

square root of (64 x^9 y^12) would be correct

Answer 13

8 x^(9/2) y^6 would be my answer

Answer 14

not an answer choice

Answer 15

2xy^2 times the square root of x
8x^4 y^6 times the square root of x
the square root of 8x^6 y^7

Answer 16

what happens when you multiply say a^b and a^c ?

Answer 17

You can throw out (a) right away because 4^(3/2) you know is 8

Answer 18

\[\large a^b \times a^c = a^{b+c}\]

Answer 19

not quite getting it. there's a even more simplified version then my answer though right?

Answer 20

The most simplified version is the answer I gave

Answer 21

\[8x^{9 \over 2}y^6=8x^4y^6 \sqrt{x}\]

Answer 22

9/2 equal 4.5 which is 4 + 0.5. so using the other formula I provided for the multiplication of exponents with the same base, you get this answer

Answer 23

These are things you have to memorize and validate with a calculator. you can prove this by writing it all out if you want. Or you can memorize these rules

Answer 24

so .5= square root of x?