Simplify the following expression: (4ab^2)^2?

Hi,

For this question, let's re-write the given expression as follows:

[4ab^2][4ab^2]

Now, recall, when multiplying quantities of the same base, we need to add the exponents:

16[a^2][b^4] <==== FINAL ANSWER

I hope that helps you out! Please let me know if you have any other questions!

4x4=16, axa=a^2, b^2xb^2=b^4;
=16a^2b^4

(4ab^2)^2= 16a^2b^4

Square each of the terms within the brackets.

4^2 = 16.
a squared = a^2
b^2 squared = b^4

Answer: 16a^2b^4.

(4ab^2)^2
= (4^2)(a^2)[(b^2)^2]
= (16a^2)(b^4)
= 16a^2b^4

(16a^2)(b^4)

16a^2 b^4

That just means you have 4 * a * (b squared) all th e power 2. Or squared.
(4ab^2)^2
It simplifies by multiplying the powers inside by the power outside.
4^1 becomes 4^(1*2) = 4^2 = 16
ab^2 becomes a^2b^4
so it becomes
16a^2b^4
:-)

OKay to simplify all you have to do is square everything inside the parentheses separately so...

4^2 = 16

a^2 = a^2

(b^2)^2 = b^4
(when you take the power of something that already has an exponent, you just multiply the exponents together... here you did 2X2 = 4)

now put it all together...

ANSWER: 16a^2b^4

Basically you distribute the exponent to everything inside the parenthesis.

( 4 a b ² ) ( 4 a b ² ) = 16 a^2 b^4