In Exercises 85–116, simplify each exponential expression. 30x²y⁵/-6x⁸y⁻³

Key Concepts

Exponential Rules

Exponential rules govern how to simplify expressions involving powers. Key rules include the product of powers (a^m * a^n = a^(m+n)), the quotient of powers (a^m / a^n = a^(m-n)), and the power of a power (a^(m^n) = a^(m*n)). Understanding these rules is essential for manipulating and simplifying exponential expressions effectively.

Simplifying Fractions

Simplifying fractions involves reducing the numerator and denominator by their greatest common factor (GCF). In the context of algebraic expressions, this means factoring out common terms and canceling them. This process is crucial for obtaining a simpler form of the expression, making it easier to analyze or compute.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent (a^(-n) = 1/a^n). This concept is important when simplifying expressions that contain negative exponents, as it allows for the transformation of the expression into a more manageable form, often involving fractions.