Question

Please help


Let a and b be positive integers. 23a×23b=?

Answer 1

The bases are the same, so we add the exponents

The answer is
`23^(a+b)` which is choice A

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Here's an example of why we add the exponents

Lets say we want to multiply 7^2 with 7^3

7^2 = 7*7

7^3 = 7*7*7

We have two copies of "7" being multiplied with 7^2, then we have an additional three copies of "7" with 7^3. Overall there are 2+3 = 5 copies of "7" that we multiply out.

So,

7^2*7^3 = (7^2) * (7^3)

7^2*7^3 = (7*7) * (7*7*7)

7^2*7^3 = 7*7*7*7*7

7^2*7^3 = 7^5

This example is fairly small in that we don't have that many copies of the base being multiplied. For larger examples, its best to use the formula mentioned

a^b*a^c = a^(b+c)

Answer 2

A) 23^(a+b)

Explanation:

if you multiply a number with diferrent exponents, the exponents will always add.