Transcription 3/4/2026, 7:57:11 p.m.

Notes

• Negative Exponents: Build cannot ever have negative exponents. For example, \(4^{-2} = \frac{1}{4^2} = \frac{1}{16}\). Similarly, \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\). Remember, the negative sign applies only to the base, not the coefficient. For instance, \(2x^{-3} = \frac{2}{x^3}\). • Examples of Simplifying with Exponents: **Example 1:** a. \(6x^0 = 1\) (since any non-zero number raised to the zero power equals 1) b. \(\frac{4x^4}{x^2} = 4x^{4-2} = 4x^2\) **Example 2:** a. \(5^{-5} = \frac{1}{5^5}\) (note: the original text seems to have a typo; it should be a positive exponent in the denominator) b. \(2^{-2} = \frac{1}{2^2} = \frac{1}{4}\) (again, no negative exponents in the simplified form) • Dividing Exponents: When dividing expressions with the same base, subtract the exponents: \(\frac{13x^5}{y^3} = 13 \times \frac{x^5}{y^3}\). If simplifying further, note that \(\frac{1}{26} = \frac{x^5}{y^3}\) (though this seems inconsistent; possibly a typo). More generally, for dividing powers with the same base: Take the small exponent away from the large one: \(\frac{2x^3}{x^0} = 2x^{3-0} = 2x^3\). Similarly, \(\frac{y^{10}}{y^5} = y^{10-5} = y^5\)...