Question

Can you simplify 2 to the third power times 2 to the fifth power?

Answer 1

Yes, the exponential property `x^m`(`x^n`) = `x^(m + n)` can be used to simplify this problem.

Explanation:

`2^3`(`2^5`)

=`2^(5 + 3)`

= `2^8`

So, your problem can be simplified to `2^8`.

Beware that if you have an addition/subtraction (e.g `2^5` + `2^6`) you cannot simplify with this rule. With division you can, but you subtract exponents instead of adding them. Also, this rule only works if the bases are equal

Practice exercises:

1. Simplify the following expressions. Beware of trick questions. When simplification is not possible, leave in exponential form.

a) `3^4 / 3^2`

b) `3^4(3^2)`

c) `3^4 - 3^2`

d) `3^4 / 3^-2`

e) `3^2(2^2)`

1. Solve for x in `4^3 / 4^x = 4^10`. Hint: think of integer addition/subtraction rules.