Question

If two numbers' bases are same, can their powers be added, subtracted, multiplied or divided?
For example-
${ 2}^{2} + { 2}^{3}$
Can the same be done when the powers are same, but bases are different?
For example-
$5 ^{2} + {6}^{2}$
(Note- The numbers are being added)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

In the first case

$2 ^{2} + {2}^{3} = 12(2 \times 2 \times 3) \\..hence \: not \: possible$

in the second case

$5 {}^{2} + 6 {}^{2} =61(which \: is \: a \: prime \: \\ number \: with \: no \: factors) \\ \\ ..hence \: not \: possible$