Exponent Rule

Definition

The exponent rule is a mathematical principle that describes how to simplify expressions involving exponents. It provides a set of guidelines for manipulating and evaluating expressions with powers or exponents.

5 Must Know Facts For Your Next Test

1. The exponent rule is particularly important when dividing monomials, as it simplifies the process of manipulating exponents.
2. When dividing monomials with the same base, the exponents are subtracted to obtain the resulting exponent.
3. Raising a power to a power involves multiplying the exponents.
4. The zero power rule states that any non-zero number raised to the power of zero is equal to 1.
5. Negative exponents represent the reciprocal of the base raised to the positive exponent.

Review Questions

• Explain how the exponent rule can be applied when dividing monomials.
  • When dividing monomials with the same base, the exponent rule states that the exponents are subtracted. For example, if dividing $x^5$ by $x^3$, the resulting expression would be $x^{5-3} = x^2$. This simplifies the division process by allowing you to subtract the exponents instead of performing long division.
• Describe the relationship between raising a power to a power and the resulting exponent.
  • The exponent rule for raising a power to a power involves multiplying the exponents. For instance, if you have $(x^5)^3$, the exponent rule states that this is equal to $x^{5 \times 3} = x^{15}$. This rule allows you to simplify complex expressions with multiple layers of exponents by multiplying the exponents together.
• Analyze the implications of the zero power rule and negative exponents in the context of dividing monomials.
  • The zero power rule states that any non-zero number raised to the power of zero is equal to 1. This means that when dividing monomials, if the exponents cancel out completely, the result will be 1. Additionally, negative exponents represent the reciprocal of the base raised to the positive exponent. This is important when dividing monomials, as it allows you to rewrite the expression using a positive exponent in the denominator, simplifying the calculation.

Related terms

Power: A power is the result of multiplying a number by itself a certain number of times, represented by an exponent.

Exponent: An exponent is the small number written to the right of and above a base number, indicating the number of times the base is to be multiplied by itself.

Monomial: A monomial is an algebraic expression with a single term, consisting of coefficients, variables, and exponents.