Question

How does multiplying powers with the same base differ from multiplying powers with the same exponent but different bases? Put this in dummy words so I can understand it please

Answer 1

Multiplying powers with the same base is simply adding their exponents/powers. For example,

$5^3\times5^6=5^{3+6}=5^9^{}^{}$

On the other hand, multiplying the same exponent but different bases is another story. For instance,

$5^2\times2^2$

To solve this one, we multiply first the two bases and the result will be raise to the given common exponent.

$(5\times2)^2=(10)^2$