If $a = 3, b = 7,$ then find the value of $a^{b} - b^{a}$

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Solution

Given that, $a = 3, b = 7,$

To find : $a^{b} - b^{a}$

$a^{b} - b^{a} = 3^{7} - 7^{3}$ (where $a = 3, b = 7$ )

$= 3 \times 3 \times 3 - 7 \times 7 \times 7$

$= 9 \times 3 - 49 \times 7$

$= 27 - 343 = - 316$

$∴ a^{b} - b^{a} = - 316$

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