Simplify each exponential expression in Exercises 23–64. $x^{14}/x^7$

Verified step by step guidance

1. Identify the rule for dividing exponential expressions with the same base: when dividing, subtract the exponents. This rule is written as \(\frac{a^m}{a^n} = a^{m-n}\).
2. Apply the rule to the given expression \(\frac{x^{14}}{x^{7}}\). Since the base is the same (x), subtract the exponent in the denominator from the exponent in the numerator.
3. Write the expression after subtracting the exponents: \(x^{14-7}\).
4. Simplify the exponent by performing the subtraction: \$14 - 7$.
5. Express the simplified form of the exponential expression as \(x^{7}\).

Key Concepts

Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers. One key rule is that when dividing like bases, you subtract the exponents: a^m / a^n = a^(m-n). This rule helps simplify expressions such as x^14 / x^7 by subtracting the exponents 14 and 7.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves reducing them to their simplest form by applying arithmetic and algebraic rules. In this case, simplifying x^14 / x^7 means rewriting the expression using exponent rules to make it easier to understand or use in further calculations.

Properties of Variables and Exponents

Variables represent unknown or changing quantities, and exponents indicate repeated multiplication. Understanding how variables behave under exponentiation and division is essential to correctly simplify expressions like x^14 / x^7, ensuring the variable remains consistent while adjusting the exponent.