Take me apart and then put me back together.

What is the most efficient method for simplifying the expression ?

Since x⁵=x*x*x*x*x and x³=x*x*x, then x⁵*x³=x*x*x*x*x*x*x*x=x⁸

However, expansion is not efficient, especially for large exponents.

What can you do with the exponents to avoid expansion?

1 answer

To avoid expansion with exponents, you can use the properties of exponents such as multiplication and addition rules. This will help simplify the expression efficiently.

For example, to simplify x⁵ * x³, you can apply the multiplication rule for exponents, which states that when multiplying two terms with the same base, you add their exponents.

In this case, x⁵ * x³ = x^(5+3) = x⁸.

Therefore, the most efficient method for simplifying the expression is to combine the exponents using the appropriate exponent rules.