Lesson
Notes
Negative Exponents
\(\displaystyle a^{-b}=\frac{1}{a^b}\)
Practice Problems
Express each without any negative exponents
\(\textbf{1)}\) \(9^{-1}\) The answer is \(\frac{1}{9}\)
\(\textbf{2)}\) \(\left(\frac{1}{9}\right)^{-1}\) The answer is \(9\)
\(\textbf{3)}\) \(9^{\frac{1}{2}}\) The answer is \(3\)
\(\textbf{4)}\) \(9^{-\frac{1}{2}}\) The answer is \(\frac{1}{3}\)
\(\textbf{5)}\) \(\left(\frac{1}{9}\right)^{\frac{1}{2}}\) The answer is \(\frac{1}{3}\)
\(\textbf{6)}\) \(\left(\frac{1}{9}\right)^{-\frac{1}{2}}\) The answer is \(3\)
\(\textbf{7)}\) \(5^{-2}\) The answer is \(\frac{1}{25}\)
\(\textbf{8)}\) \(\displaystyle \left(\frac{1}{4}\right) ^{-2} \) The answer is \(16\)
\(\textbf{9)}\) \(\displaystyle \left(\frac{1}{4}\right) ^{-1/2} \) The answer is \(2\)
\(\,\,\,\,\,\,\displaystyle \left(\frac{1}{4}\right) ^{-1/2}\)
\(\,\,\,\,\,\,\displaystyle \left(\frac{4}{1}\right) ^{1/2}\)
\(\,\,\,\,\,\,\displaystyle \left(4\right) ^{1/2}\)
\(\,\,\,\,\,\,\displaystyle \sqrt{4} \)
\(\,\,\,\,\,\,\displaystyle 2 \)
\(\,\,\,\,\,\,\displaystyle \left(\frac{1}{4}\right) ^{-1/2}\)
\(\,\,\,\,\,\,\displaystyle \left(\frac{4}{1}\right) ^{1/2}\)
\(\,\,\,\,\,\,\displaystyle \left(4\right) ^{1/2}\)
\(\,\,\,\,\,\,\displaystyle \sqrt{4} \)
\(\,\,\,\,\,\,\displaystyle 2 \)
\(\textbf{10)}\) \(4^{-1/2}\) The answer is \(\frac{1}{2}\)
\(\textbf{11)}\) \( (2z^3 w^6 )^{-4} \)
The answer is \( \displaystyle\frac{1}{16z^{12} w^{24}}\)![Link to Youtube Video Solving Question Number 11](https://andymath.com/wp-content/uploads/2020/08/play-video.jpg")
\(\textbf{12)}\) \( \displaystyle \left(\frac{4}{9}\right) ^{-1/2} \) The answer is \( \displaystyle \frac{3}{2} \)
\(\textbf{13)}\) \( \displaystyle\frac{4x^4 y^{-2} z}{6x^{-1} yz} \) The answer is \( \displaystyle\frac{2x^5}{3y^3} \)
\(\textbf{14)}\) \( \displaystyle \left(\frac{5x^5 y^{-3} z^2}{6x^{-2} yz} \right)^{-2} \) The answer is \( \displaystyle\frac{36y^8}{25x^{14} z^2} \)
\(\textbf{15)}\) \( 3^{-4} \div 3^{-8} \) The answer is \( 3^4=81 \)
\(\)\,\,\,\,\,3^{-4} \div 3^{-8}\(\)
\(\)\,\,\,\,\,\displaystyle\frac{1}{3^4} \div \frac{1}{3^8}\(\)
\(\)\,\,\,\,\,\displaystyle\frac{1}{3^4} \times \frac{3^8}{1}\(\)
\(\)\,\,\,\,\,\displaystyle\frac{3^8}{3^4}\(\)
\(\)\,\,\,\,\,3^8-4\(\)
\(\)\,\,\,\,\,3^4=81\(\)
\(\)\,\,\,\,\,3^{-4} \div 3^{-8}\(\)
\(\)\,\,\,\,\,\displaystyle\frac{1}{3^4} \div \frac{1}{3^8}\(\)
\(\)\,\,\,\,\,\displaystyle\frac{1}{3^4} \times \frac{3^8}{1}\(\)
\(\)\,\,\,\,\,\displaystyle\frac{3^8}{3^4}\(\)
\(\)\,\,\,\,\,3^8-4\(\)
\(\)\,\,\,\,\,3^4=81\(\)
See Related Pages\(\)
\(\bullet\text{ Intro to Exponents}\)
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\(\bullet\text{ Zero Exponents}\)
\(\,\,\,\,\,\,\,\,3^{0}=1…\)
\(\bullet\text{ Rational Exponents}\)
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