Simplify each exponential expression in Exercises 23–64. x^−5⋅x^10

Key Concepts

Exponential Rules

Exponential rules are fundamental properties that govern the operations of exponents. Key rules include the product of powers rule, which states that when multiplying two expressions with the same base, you add their exponents. For example, x^a ⋅ x^b = x^(a+b). Understanding these rules is essential for simplifying expressions involving exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For instance, x^−n = 1/x^n. This concept is crucial when simplifying expressions that contain negative exponents, as it allows for rewriting them in a more manageable form, often leading to a clearer final expression.

Combining Like Terms

Combining like terms involves simplifying expressions by merging terms that have the same base and exponent. In the context of exponents, this means applying the product of powers rule to consolidate terms. This process is vital for achieving a simplified expression, making it easier to interpret and work with in further calculations.