Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. r^7/r^10

Verified step by step guidance

1. Step 1: Identify the expression to simplify, which is $\frac{r^7}{r^{10}}$.
2. Step 2: Apply the quotient rule for exponents, which states $\frac{a^m}{a^n}=a^{m-n}$.
3. Step 3: Subtract the exponents in the expression: $7-10$.
4. Step 4: Simplify the expression to $r^{-3}$.
5. Step 5: Convert the expression to have positive exponents: $\frac{1}{r^3}$.

Key Concepts

Exponent Rules

Exponent rules are mathematical guidelines that dictate how to handle operations involving powers of numbers or variables. Key rules include the product of powers (adding exponents), the quotient of powers (subtracting exponents), and the power of a power (multiplying exponents). Understanding these rules is essential for simplifying expressions with exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^-n = 1/a^n. In simplification, it is important to express answers without negative exponents, which often involves rewriting the expression to ensure all terms are in positive exponent form.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions to their simplest form by canceling common factors in the numerator and denominator. This process often requires applying exponent rules to combine like terms and ensure that the final expression is presented clearly, adhering to the requirement of non-negative exponents.