Question

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

Answer 1

They are not equal based on some properties in indices

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

Answer 2

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.