Fill in the blanks. The quotient rule for exponents states that \( \frac{b^{m}}{b^{n}}= \) \( \qquad \) , \( \mathrm{b}=0 \). When dividing exponential expressions with the same nonzero base, \( \qquad \) the exponents. The quotient rule for exponents states that \( \frac{b^{m}}{b^{n}}= \) \( \square \) . \( b \geq 0 \). When dividing exponential expressions with the same nonzero base, \( \square \) the exponents.

Certainly! Here are the filled-in blanks for the quotient rule of exponents: The quotient rule for exponents states that \( \frac{b^{m}}{b^{n}}= \) \( \boxed{b^{m - n}} \). \( b \neq 0 \). When dividing exponential expressions with the same nonzero base, \( \boxed{\text{subtract}} \) the exponents. **Explanation:** 1. **First Blank (\( \frac{b^{m}}{b^{n}}= \boxed{b^{m - n}} \)):** - **Quotient Rule:** When you divide two expressions that have the same base, you subtract the exponent in the denominator from the exponent in the numerator. Mathematically, this is expressed as: \[ \frac{b^{m}}{b^{n}} = b^{m - n} \] 2. **Second Blank (When dividing exponential expressions with the same nonzero base, \( \boxed{\text{subtract}} \) the exponents.):** - **Action on Exponents:** The specific operation you perform on the exponents when applying the quotient rule is **subtraction**. This means you take the exponent of the denominator and subtract it from the exponent of the numerator. **Final Statement:** The quotient rule for exponents states that \( \frac{b^{m}}{b^{n}}= b^{m - n} \), \( b \neq 0 \). When dividing exponential expressions with the same nonzero base, subtract the exponents.