Question

EValuate each expression. $$\frac{3 ! \cdot 5 ! \cdot 7 !}{1 ! 8 !}$$

   EValuate each expression.
$$\frac{3 ! \cdot 5 ! \cdot 7 !}{1 ! 8 !}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 18

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

We know that $8!$ is equal to $8 \times 7!$. So, we can rewrite the expression as follows: $$\frac{3 ! \cdot 5 ! \cdot 7 !}{1 ! 8 !} = \frac{3 ! \cdot 5 ! \cdot 7 !}{1 ! \cdot 8 \cdot 7 !}$$ Show more…

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EValuate each expression. $$\frac{3 ! \cdot 5 ! \cdot 7 !}{1 ! 8 !}$$

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Key Concepts

Algebraic Simplification

Algebraic simplification involves manipulating mathematical expressions to a simpler form. This includes techniques such as factoring, canceling common factors, and rewriting expressions to reveal underlying structures, which is critical when evaluating complex factorial expressions.

Factorial Notation

Factorial notation, represented by an exclamation mark (n!), is used to denote the product of all positive integers from 1 to n. This concept is fundamental in combinatorics, probability, and many mathematical formulas, helping in counting arrangements and sequences.

Cancellation in Factorial Expressions

When working with expressions involving factorials, a common technique is to cancel out similar terms in the numerator and denominator. By expressing larger factorials in terms of smaller ones, one can simplify the expression significantly, reducing the computational complexity.

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