Quotient rule of exponents practice

Answer 1

The quotient rule of exponents states that when you divide two expressions with the same base, you subtract the exponents. Mathematically, it is expressed as:

\[ \frac{a^m}{a^n} = a^{m-n} \quad (a \neq 0) \]

Here are some practice problems for you to work on:

Problems

1. Simplify \(\frac{x^5}{x^2}\).
2. Simplify \(\frac{a^8}{a^3}\).
3. Simplify \(\frac{y^{10}}{y^4}\).
4. Simplify \(\frac{z^{12}}{z^{12}}\).
5. Simplify \(\frac{m^7}{m^2}\).
6. Simplify \(\frac{p^9}{p^{11}}\).
7. Simplify \(\frac{b^5}{b^5}\).
8. Simplify \(\frac{x^6}{x^0}\).
9. Simplify \(\frac{10^4}{10^1}\).
10. Simplify \(\frac{a^2b^3}{a^1b^2}\).

Solutions

1. \(\frac{x^5}{x^2} = x^{5-2} = x^3\)
2. \(\frac{a^8}{a^3} = a^{8-3} = a^5\)
3. \(\frac{y^{10}}{y^4} = y^{10-4} = y^6\)
4. \(\frac{z^{12}}{z^{12}} = z^{12-12} = z^0 = 1\)
5. \(\frac{m^7}{m^2} = m^{7-2} = m^5\)
6. \(\frac{p^9}{p^{11}} = p^{9-11} = p^{-2}\)
7. \(\frac{b^5}{b^5} = b^{5-5} = b^0 = 1\)
8. \(\frac{x^6}{x^0} = x^{6-0} = x^6\)
9. \(\frac{10^4}{10^1} = 10^{4-1} = 10^3\)
10. \(\frac{a^2b^3}{a^1b^2} = a^{2-1}b^{3-2} = a^1b^1 = ab\)

Feel free to ask more questions or for clarifications!