Question

a2b3, a2b3,b2a3,b3a2 are they same

Answer 1

No....

they can be rearranged as

a2b3, a2b3, a3b2, a2 31

The third one is odd one out.

Hope this helps

Answer 2

Correct question:

Expand: a²b³, a²b³, b²a³, b³a². are they same ?

Solution:

$\sf{\longrightarrow a {}^{3}b {}^{2} = a {}^{3} \times b {}^{2} } \\ \sf {\longrightarrow ( a \times a \times a) \times (b \times b)} \\ \sf{\longrightarrow a\times a \times a \times b \times b} \\ \\ \sf{\longrightarrow a {}^{2} b {}^{3} = a {}^{2} \times b {}^{3}} \\ \sf{\longrightarrow a \times a \times b \times b \times b} \\ \\ \sf{\longrightarrow b {}^{2} a {}^{3} = b {}^{2} \times a {}^{3}} \\ \sf{\longrightarrow b \times b \times a \times a \times a} \\ \\ \sf{\longrightarrow b {}^{3} a {}^{2} = b {}^{3} \times a {}^{2}} \\ \sf{\longrightarrow b \times b \times b \times a \times a}$

Addional information:

The powers "a^3 b^2" , "a^2 b^3" are of a and b, both are different. Also, the powers are diffrent. But also In other way "a^3 b^2" , "a^2 b^3" are same it is because the two terms are same.

$\sf{a {}^{3} b {}^{2} = a {}^{3} \times b {}^{2} = b {}^{2} \times a {}^{3} = b {}^{2} a {}^{3}}$

Finally,

$\sf\boxed{{{a {}^{2} b {}^{3} \: \: and \: \: \: b {}^{3} a {}^{2} \: \: are \: same}}}$