# Intergers and Eponents

• Nov 24th 2006, 12:17 PM
Kitty_Kat
Intergers and Eponents
Please tell me the steps to get through these questions;

1) (8.9x10 to the exponent 5) to the exponent 4

2) (4x10 the the eponent negative 5) to the exponent negative 6

3) (6x10 to the exponent negative 5) to the exponent 3

All help is greatly appreciated.
• Nov 24th 2006, 12:33 PM
Ranger SVO
1. 890,000 and 89,000
See a pattern, simply move the decimal to the right 5 places for the first one or 4 places for the second one

2. 0.00004 and 0.000004
now we move the decimal place to the left 5 places for the first one and 6 places for the second one.

negative exponent move left
posite exponent move right

Bet you can get the next one.
• Nov 24th 2006, 12:38 PM
Quick
Quote:

Originally Posted by Kitty_Kat
Please tell me the steps to get through these questions;

1) (8.9x10 to the exponent 5) to the exponent 4

2) (4x10 the the eponent negative 5) to the exponent negative 6

3) (6x10 to the exponent negative 5) to the exponent 3

All help is greatly appreciated.

You need to know this property: $\displaystyle \left(x^a\right)^b=x^{(ab)}$

So: $\displaystyle \left(8.9\times10^5\right)^4=8.9\times10^{(5\times 4)}=8.9\times10^{20}$

EDIT: Wow, I completely forgot to distribute the exponent :(
• Nov 24th 2006, 03:11 PM
Soroban
Hello, Kitty_Kat!

You didn't give us any instructions.
I will assume the answers are to be in Scientific Notation.

Quote:

$\displaystyle 1)\;\;\left(8.9 \times 10^5\right)^4$
$\displaystyle \left(8.9 \times 10^5\right)^4\;=\;8.9^4 \times \left(10^5\right)^4 \;=\;6,274.2241 \times 10^{20} \;=\;6.2742241 \times 10^{23}$

Quote:

$\displaystyle 2)\;\;\left(4 \times 10^{-5}\right)^{-6}$
$\displaystyle \left(4\times10^{-5}\right)^{-6}\;=\;4^{-6}\times\left(10^{-5}\right)^{-6}$ $\displaystyle \;=\;0.000244140625 \times 10^{30}\;=\;2.44140625 \times 10^{26}$

Quote:

$\displaystyle 3)\;\;\left(6 \times 10^{-5}\right)^3$
$\displaystyle \left(6\times10^{-5}\right)^3\;=\;6^3\times\left(10^{-5}\right)^3\;=\;216\times10^{-15}\;=\;2.16\times10^{-13}$