Question

How do you simplify $ 90 \times 8! $ ?

Answer 1

Hint: Here in this question, they have used $ \times $ operator. This operator does the multiplication and we are multiplying the two terms. In this question we also see ! symbol this represents the factorial, the factorial is defined as $ n! = n \times (n - 1) \times (n - 2) \times ... \times 2 \times 1 $ .

Complete step-by-step answer:
Here in this question, they have used a multiplication symbol. We have mathematical operations namely addition, subtraction, multiplication and division. + represents the addition, - represents subtraction, $ \times $ represents the multiplication and $ \div $ represents the division. The multiplication is a repeated addition.
Now consider $ 90 \times 8! $
First we simplify the factorial term. ! indicates the factorial. In general the factorial is defined as $ n! = n \times (n - 1) \times (n - 2) \times ... \times 2 \times 1 $ where n is a positive integer.
First we simplify the factorial term, so we have
 $ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 $
We multiply two-two terms, when we multiply 8 to 7 we have
 $ \Rightarrow 8! = 56 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 $
On multiplying 56 and 6 we get
 $ \Rightarrow 8! = 336 \times 5 \times 4 \times 3 \times 2 \times 1 $
On multiplying 336 and 5 we get
 $ \Rightarrow 8! = 1680 \times 4 \times 3 \times 2 \times 1 $
On multiplying 1680 and 4 we get
 $ \Rightarrow 8! = 6720 \times 3 \times 2 \times 1 $
On multiplying 6720 and 3 we get
 $ \Rightarrow 8! = 20160 \times 2 \times 1 $
On multiplying 20160 and 2 we get
 $ \Rightarrow 8! = 40320 \times 1 $
On multiplying 40320 and 1 we get
 $ \Rightarrow 8! = 40320 $
Now we have simplified the factorial term
Therefore $ 8! = 40320 $
Now we have to multiply 90 to the factorial of 8.
 $ 90 \times 8! $
Substitute the value of 8 factorial we get
 $ \Rightarrow 90 \times 40320 $
On multiplying 90 and 40320 we get
 $ \Rightarrow 3628800 $
hence, we have simplified the given question and determined the value
therefore $ 90 \times 8! = 3628800 $
So, the correct answer is “3628800”.

Note: To solve the mathematical problems we have mathematical operations. There are for mathematical operations namely addition, subtraction, multiplication and division. + represents the addition, - represents subtraction, $ \times $ represents the multiplication and $ \div $ represents the division. The multiplication is the repeated addition. ! indicates the factorial. In general the factorial is defined as $ n! = n \times (n - 1) \times (n - 2) \times ... \times 2 \times 1 $ where n is a positive integer.