Question

I need the answer please help me.

Q1) explain how can you write a quotient of powers using a single power. use your examples to illustrate your explanation

Q2) A crawlspace in each station has the space of a rectangular prism. it is about 100 cm high, 10 cm wide and 1 km long. what is the volume enclosed by the crawlspace?

Q3)What is the probability of rolling eight perfect squares in a row

Answer 1

Q1)
`a^(m)` /
`a^(n)` =
`a^(m-n)`

Q2)
`10^(8)` cm cube

Q3) 0.000152

Explanation:

Step 1:

Q1)

Quotient of power rule indicates that when we are dividing 2 exponents with the base which are same but different powers, the answer would have the same base and the exponent would be the difference in power.

For example
`a^(m)` /
`a^(n)` =
`a^(m-n)`

`4^(8)`/
`4^(3)` =
`4^(8-3)` =
`4^(5)`

Step 2 :

Q2)

The volume of the given rectangular prism is the height multiplied by the width multiplied by the length

= 100 * 10 * 100000 = 100000000 =
`10^(8)` cm cube. [Given h = 1 cm, w = 10 cm, l = 1 km = 100000cm]

Step 3 :

Q3)

Probability of obtaining a perfect square in a single roll of a die is 2/6 (As the total number of outcome is 6 and number of favorable outcome is 2 (perfect squares are 1 and 4)

Hence probability of obtaining eight perfect squares are
`(1/3)^(8)` = 0.000152