Question

Please can you give me the answers to the questions above in standard form.​

Answer 1

a)
`4.5 * 10^(11)`

b)
`3.5 * 10^(3)`

Explanation:

a) We have to simplify the below expression in standard form.

The expression is
`(5* 10^(3)) * (9 * 10^(7))`

Now,
`(5* 10^(3)) * (9 * 10^(7))`

=
`(9 * 5) * (10^(3) * 10^(7))`

=
`45 * 10^((3 + 7))` {Since
`a^(b) * a^(c) = a^((b + c))`}

=
`45 * 10^(10)`

=
`4.5 * 10^(11)` (Answer)

b) We have to simplify the below expression in standard form.

The expression is
`(7* 10^(5)) / (2 * 10^(2))`

Now,
`(7* 10^(5)) / (2 * 10^(2))`

=
`(7 / 2) * (10^(5) / 10^(2))`

=
`3.5 * 10^((5 - 2))` {Since
`a^(b)/ a^(c) = a^((b - c))`}

=
`3.5 * 10^(3)` (Answer)