Evaluate each exponential expression in Exercises 1–22. 2^3/2^7

Key Concepts

Exponential Expressions

Exponential expressions are mathematical expressions that involve a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression 2^3, the base is 2 and the exponent is 3, meaning 2 is multiplied by itself three times (2 × 2 × 2). Understanding how to manipulate these expressions is crucial for evaluating them correctly.

Properties of Exponents

The properties of exponents are rules that simplify the operations involving exponential expressions. Key properties 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). These properties allow for easier calculations and simplifications when evaluating expressions like 2^3 / 2^7.

Simplifying Fractions

Simplifying fractions involves reducing them to their simplest form, where the numerator and denominator have no common factors other than 1. In the context of exponential expressions, this means applying the properties of exponents to combine the bases and adjust the exponents accordingly. For instance, in the expression 2^3 / 2^7, you would subtract the exponents to simplify it to 2^(3-7) = 2^(-4).