Math Problem Statement
Simplify each of the following expressions: (5x)^2, (4y)^3, (7ab)^2, (-2x)^3, (-2x)^4, (10ab)^4, (6xyz)^2, (-xy)^5, (7rs)^3, (5x)^{-2}
Solution
Let's solve each of these expressions step-by-step. These involve using exponent rules for products, such as:
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5.
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10.
If you need further clarifications or additional explanations, feel free to ask!
Related Questions:
- What happens when an exponent is zero?
- How do negative exponents affect the expression?
- What is the rule for raising a product to a power?
- How do exponents apply to fractional bases?
- What happens if an exponent is negative and the base includes a negative number?
Tip: When raising a product to a power, apply the exponent to each factor individually to simplify the expression.
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Math Problem Analysis
Mathematical Concepts
Exponents
Algebra
Simplifying Expressions
Formulas
(a * b)^n = a^n * b^n
Negative exponent rule: a^{-n} = 1 / a^n
Power of a product rule: (ab)^n = a^n * b^n
Theorems
Exponent Rules
Suitable Grade Level
Grades 7-9