Question

Anyone know how to do BOTH of these? Thanks!

Answer 1

The answer to the top one is 243.

Answer 2

Question 1:

We have to simplify the expression
`((3^(3) * 3^(4))^(2))/(3^(3) * 9^(3))`

=
`((3^(3))^(2) * (3^(4))^(2))/(3^(3) * (3^(2))^(3))`

(Using the law of exponent,
`(a^(m))^(n)=a^(m * n)`)

=
`(3^(6) * 3^(8))/(3^(3) * 3^(6))`

Cancelling
`3^(6)` from the numerator and denominator.

=
`(3^(8))/(3^(3))`

(Using the law of exponent,
`(a^(m))/(a^(n))=a^(m-n)`)

=
`3^(8-3)`

=
`3^(5)`

= 243

Question 2:

The average mass of an adult human = 65 kg

The average mass of an ant =
`4 * 10^(-6)` kg (Since the unit of average mass of ant is not mentioned, i have assumed it as kg)

Let the number of ants be 'n'.

According to the question,

Average mass of adult human = n
`*` Average mass of ant

`65 kg = 4 * 10^(-6) kg * n`

`n=(65)/(4 * 10^(-6))`

`n=16.25 * 10^(6)`

`n=1625 * 10^(4)`

So,
`1625 * 10^(4)` ants are needed to equal the mass of one average human.