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 $\frac{(3^{3} \times 3^{4})^{2}}{3^{3} \times 9^{3}}$

=$\frac{(3^{3})^{2} \times (3^{4})^{2}}{3^{3} \times (3^{2})^{3}}$

(Using the law of exponent, $(a^{m})^{n}=a^{m \times n}$)

=$\frac{3^{6} \times 3^{8}}{3^{3} \times 3^{6}}$

Cancelling $3^{6}$ from the numerator and denominator.

=$\frac{3^{8}}{3^{3}}$

(Using the law of exponent, $\frac{a^{m}}{a^{n}}=a^{m-n}$)

=$3^{8-3}$

=$3^{5}$

= 243

Question 2:

The average mass of an adult human = 65 kg

The average mass of an ant = $4 \times 10^{-6}$ 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 $\times$ Average mass of ant

$65 kg = 4 \times 10^{-6} kg \times n$

$n=\frac{65}{4 \times 10^{-6}}$

$n=16.25 \times 10^{6}$

$n=1625 \times 10^{4}$

So, $1625 \times 10^{4}$ ants are needed to equal the mass of one average human.