Question

Show all your work which is the simplest form of the expression below

Answer 1

Answer: 2³

Explanation:

We will use the order of operations to help us solve. This means, in this case, starting with exponents and then multiplying. We will also use the exponent rules.

Given:

`\displaystyle (2^2)^4\;*\;2^(-5)`

Power rule of exponents:

`\displaystyle (2^2)^4\;*\;2^(-5)=(2^(2*4))\;*\;2^(-5)`

`(2^(8))\;*\;2^(-5)`

Product rule of exponents:

`\displaystyle (2^(8))\;*\;2^(-5) = (2^(8+-5))= (2^(8-5))`

`(2^(3))`

The simplified form of the expression, from the given options, is 2³.