Here are the essential concepts you must grasp in order to answer the question correctly.
Quotients-to-Powers Rule
The quotients-to-powers rule states that when raising a fraction to a power, you can apply the exponent to both the numerator and the denominator separately. This means that for any expression of the form (a/b)ⁿ, it can be simplified to aⁿ/bⁿ. This rule is essential for simplifying expressions involving fractions raised to exponents.
Recommended video:
Product, Quotient, and Power Rules of Logs
Exponent Rules
Exponent rules are a set of mathematical principles that govern how to manipulate powers and roots. Key rules include the product of powers, power of a power, and power of a product. Understanding these rules is crucial for simplifying expressions, especially when dealing with multiple terms raised to exponents, as they dictate how to combine and simplify these terms effectively.
Recommended video:
Introduction to Exponent Rules
Negative Exponents
Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, x⁻ⁿ = 1/xⁿ. This concept is important when simplifying expressions, as it allows for the transformation of terms that may appear in the denominator into a more manageable form in the numerator, facilitating easier simplification of the overall expression.
Recommended video: