Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Powers
Exponents represent repeated multiplication of a base number. The power indicates how many times the base is multiplied by itself. Understanding the laws of exponents, such as the product of powers and power of a power, is essential for simplifying expressions involving exponents.
Recommended video:
Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, x⁻ⁿ = 1/xⁿ. This concept is crucial when simplifying expressions with negative exponents, as it allows for rewriting them in a more manageable form.
Recommended video:
Products-to-Powers Rule
The products-to-powers rule states that when raising a product to a power, you can distribute the exponent to each factor in the product. For instance, (ab)ⁿ = aⁿbⁿ. This rule is vital for simplifying expressions like (-3x⁻²)⁻³, as it allows for the individual simplification of each component.
Recommended video:
Product, Quotient, and Power Rules of Logs