Question

Evaluate the following expression.

2^-3

Answer 1

hey! Long time no see ! :D

Answer 2

Hi!

Answer 3

so we are given the problem \[\LARGE 2^{-3} \]
negative exponents aren't allowed, so we have to take the reciprocal.

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.
For example \[ \LARGE x^{-2} \rightarrow \frac{1}{x^2} \]

Answer 4

so we need to flip \[\LARGE 2^{-3} \] and that becomes ..?

Answer 5

-3 over 2?

Answer 6

not exactly...
remember our example
\[\LARGE x^{-2} \rightarrow \frac{1}{x^2} \]

so let x =2 and replace the -2 with -3

Answer 7

A negative exponent is equivalent to the inverse of the same number with a positive exponent

Answer 8

example
\[\LARGE x^{-4} \rightarrow \frac{1}{x^4} \]

Answer 9

Oh okay I got it!

Answer 10

so let's try to apply the example to \[\LARGE 2^{-3} \]

Answer 11

so instead of \[\LARGE 2^{-3} \]

we have \[\LARGE 2^{-3} \rightarrow \frac{1}{?} \]