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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.

Ask by Christensen Bartlett. in the United States
Jan 24,2025

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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.

Solución

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.

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Bonus Knowledge

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. When you see divisions with exponents, just remember: you can keep calm and simplify by subtracting! It's like having a little math magic that simplifies your life. Just don't confuse it with the addition rule – that’s a whole different party! And if you mix up the rules, don’t fret! Even the best of us have been there. Just remember that each operation has its own rule-brush to make the division neat and tidy. So next time you break out the quotient rule, be sure to wear your thinking cap!

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