Simplify and write the resulting expression with only positive exponents. -2 x^2(-2 x^3)^5

Name: Problem 48, Chapter 0: Algebra and Trigonometry
Uploaded: 2021-06-14T21:47:23-08:00
Duration: 2 min 26 s
Channel: Michael Cooper
Description: Simplify and write the resulting expression with only positive exponents. -2 x^2(-2 x^3)^5

step 1 In this exercise, we are using properties of exponents to simplify this product. I want to use o

Simplify and write the resulting expression with only...

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Key Concepts

Exponentiation Rules

Exponentiation rules govern how powers are distributed over products and how exponents are manipulated. These rules include properties like (a^m)^n = a^(mn) and a^m * a^n = a^(m+n), which are essential for simplifying expressions involving powers.

Power of a Product Rule

The power of a product rule states that when a product is raised to a power, each factor within the product is raised to that power separately, i.e., (ab)^n = a^n * b^n. This rule is crucial when simplifying expressions with variables and coefficients inside parentheses raised to a power.

Handling Negative Bases in Exponentiation

When an expression with a negative base is raised to a power, it is important to consider the parity of the exponent. If the exponent is even, the result is positive, and if it is odd, the result remains negative. This understanding is vital for correctly simplifying and determining the sign of the resulting expression.

Multiplying Monomials

Multiplying monomials involves combining like factors, especially when variables with exponents are multiplied together. This is done by multiplying coefficients and adding the exponents of the same base, which ensures that the expression is correctly simplified and presented with only positive exponents.

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