Question 1:
We have to simplify the expression [tex] \frac{(3^{3} \times 3^{4})^{2}}{3^{3} \times 9^{3}} [/tex]
=[tex] \frac{(3^{3})^{2} \times (3^{4})^{2}}{3^{3} \times (3^{2})^{3}} [/tex]
(Using the law of exponent, [tex] (a^{m})^{n}=a^{m \times n} [/tex])
=[tex] \frac{3^{6} \times 3^{8}}{3^{3} \times 3^{6}} [/tex]
Cancelling [tex] 3^{6} [/tex] from the numerator and denominator.
=[tex] \frac{3^{8}}{3^{3}} [/tex]
(Using the law of exponent, [tex] \frac{a^{m}}{a^{n}}=a^{m-n} [/tex])
=[tex] 3^{8-3} [/tex]
=[tex] 3^{5} [/tex]
= 243
Question 2:
The average mass of an adult human = 65 kg
The average mass of an ant = [tex] 4 \times 10^{-6} [/tex] 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 [tex] \times [/tex] Average mass of ant
[tex] 65 kg = 4 \times 10^{-6} kg \times n [/tex]
[tex] n=\frac{65}{4 \times 10^{-6}} [/tex]
[tex] n=16.25 \times 10^{6} [/tex]
[tex] n=1625 \times 10^{4} [/tex]
So, [tex] 1625 \times 10^{4} [/tex] ants are needed to equal the mass of one average human.
