Expand $a^{3} b^{2}, a^{2} b^{3}, b^{2} a^{3}, b^{3} a^{2}$ . Are they all same?

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Solution

STEP 1 : Expanding the exponents
$a^{3} b^{2} = a \times a \times a \times b \times b$
$a^{2} b^{3} = a \times a \times b \times b \times b$
$b^{2} a^{3} = a \times a \times a \times b \times b$
$b^{3} a^{2} = a \times a \times b \times b \times b$
STEP 2 : Comparing the above exponents
$a^{3} b^{2} = b^{2} a^{3}$ and $a^{2} b^{3} = b^{3} a^{2}$
Hence, they all are not same.

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