Question

How do you evaluate `(0.8\times 10^ { 4} ) ( 128\times 10^ { 4} )`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(0.8 xx 128) xx (10^4 xx 10^4) =>`

`102.4 xx (10^4 xx 10^4)`

Now, use this rule of exponents to multiply the 10s terms:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`102.4 xx (10^color(red)(4) xx 10^color(blue)(4)) =>`

`102.4 xx 10^((color(red)(4) + color(blue)(4))) =>`

`102.4 xx 10^8`

If we want to write this in standard scientific notation we need to move the decimal point 2 places to the left which means we need to increase the exponent of the 10s term:

`102.4 xx 10^8 => 1.024 xx 10^10`

If we want to right this in standard notation we need to move the decimal point 10 places to the right:

`1.024 xx 10^10 => 10,240,000,000`