Question

(100 POINTS)

Answer 1

Answer:

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

Step-by-step explanation:

$7^{8} \\=7\times7\times7\times7\times7\times7\times7\times7\\=5,764801\\7^{6} \\=\frac{7^{8}}{7^{2} } \\=\frac{5,764801}{49} \\=117,649$

$7\times(\frac{1}{2}+\frac{1}{2})\\ =7\times(\frac{1+1}{2})\\=7\times(\frac{2}{2})\\=7\times1\\=7$

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

Answer:

1. $\frac{7^8}{7^6}=49$

2. 7

3. 18

Step-by-step explanation:

Question 1:

Given:

The expression to simplify is $\frac{7^8}{7^6}$.

We use the property of exponent $\frac{a^m}{a^n}=a^{m-n}$

Therefore, $\frac{7^8}{7^6}=7^{8-6}=7^2=7\times 7 = 49$

Question 2:

Given:

The expression to simplify is $7(\frac{1}{2}+\frac{1}{2})$.

We add the fractions first inside the parenthesis.

So, $\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}=1$

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:

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