Consider the expressions ab^2 and a^2b^2. are the two expressions equivalent? which properties did you use to prove or disprove?

Following order of operations rules (PEMDAS) helps immeasurably with the decision making here.

ab^2 definitely means a*b^2; exponentiation takes place before multiplication.

a^2b^2 could be written as a^2*b^2; find these squares first and then multiply the two squares together.

The two expressions are not equivalent.

They are not equal based on some properties in indices

Step-by-step explanation:

Considering both expressions

ab² and a²b², this two expressions are not the same. It can be seen that in ab², only the b variable was squared but not a but in a²b², both variables a and b were squared.

In indices,

ab² ,= a×b²

a²b² = (ab)² = a² × b²

a×b² is therefore not equal to a²×b² based on the law of indices.

For example if a = 2 and b=

ab² = a × b² = 2 × 2²

= 2×4

= 8

a²b² = a²×b² = 2²×3²

= 4×9

= 36

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

step-by-step explanation:

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