Question

(100 POINTS)

1. What is the answer to 7^8
-------
7^6


2. What is 7(1/2 + 1/2)


3. What is the sum of the first 5 prime numbers?

Answer 1

1)5,764801; 117,649 2) 7 3)28

Explanation:

`7^(8) \\=7*7*7*7*7*7*7*7\\=5,764801\\7^(6) \\=(7^(8))/(7^(2) ) \\=(5,764801)/(49) \\=117,649`

`7*((1)/(2)+(1)/(2))\\ =7*((1+1)/(2))\\=7*((2)/(2))\\=7*1\\=7`

A prime number is a whole number greater than 1 whose only factors are 1 and itself

Sum of 1st five prime numbers=2+3+5+7+11

=28

Answer 2

1.
`(7^8)/(7^6)=49`

2. 7

3. 18

Explanation:

Question 1:

Given:

The expression to simplify is
`(7^8)/(7^6)`.

We use the property of exponent
`(a^m)/(a^n)=a^(m-n)`

Therefore,
`(7^8)/(7^6)=7^(8-6)=7^2=7* 7 = 49`

Question 2:

Given:

The expression to simplify is
`7((1)/(2)+(1)/(2))`.

We add the fractions first inside the parenthesis.

So,
`(1)/(2)+(1)/(2)=(1+1)/(2)=(2)/(2)=1`

Now,
`7(1)=7`

Question 3:

The first five prime numbers are 1, 2, 3, 5, and 7.

Therefore, the sum of these five numbers is given as:

`1+2+3+5+7=18`