Question

Can someone explain to me how to do negative exponents... for example

2^-3

Answer 1

\[a ^{-b} = \frac{ 1 }{ a^{b} }\]

Answer 2

What?

Answer 3

2^(-3) is the same as 1/(2^3)...

Answer 4

Or 1/(2x2x2)

Answer 5

I still dont get what your saying

Answer 6

Do you know what 2^3 is.

Answer 7

Haha I got it now thanks :) its just dividing that number as many times as the exponet

Answer 8

Rule:

\(a^{-b} = \dfrac{1}{a^b} \)

Examples:

\( 5^{-1} = \dfrac{1}{5^1} = \dfrac{1}{5} \)

\(4^{-2} = \dfrac{1}{4^2} = \dfrac{1}{16} \)

\(6^{-5} = \dfrac{1}{6^5} \)

Answer 9

This is one way of thinking of negative exponents.

In this example I started with \(5^4\).

After the first line, each line is 5 times smaller that the line above.

\(5^4 = 5 \times 5 \times 5 \times 5 = 625 \)

\(5^3 = 5 \times 5 \times 5 = 125\)

\(5^2 = 5 \times 5 = 25\)

\(5^1 = 5 \)

\(5^0 = 1 \)

\(5^{-1} = \dfrac{1}{5} \)

\(5^{-2} = \dfrac{1}{5 \times 5}=\dfrac{1}{25} \)

\(5^{-3} = \dfrac{1}{5 \times 5 \times 5}=\dfrac{1}{125} \)

Etc.