Notes
| \({\text{Exponents Properties}}\) |
| \(\underline{\text{Notes}}\) |
\(\underline{\text{Examples}}\) |
| \(\displaystyle k^ak^b=k^{a+b}\) |
\(\displaystyle 7^2\cdot7^3=7^{2+3}=7^5\) |
| \(\displaystyle \left(k^a \right)^b=k^{a \cdot b}\) |
\(\displaystyle \left(7^2 \right)^3=7^{2 \cdot 3}=7^6\) |
| \(\displaystyle \left(km \right)^a=k^a \cdot m^a\) |
\(\displaystyle \left(7x \right)^3=7^3 \cdot x^3=343x^3\) |
| \(\displaystyle \frac{k^a}{k^b}=k^{a-b}\) |
\(\displaystyle \frac{7^5}{7^3}=7^{5-3}=7^2=49\) |
| \(\displaystyle \left( \frac{k}{m} \right)^a=\frac{k^a}{m^a}\) |
\(\displaystyle \left( \frac{2}{3} \right)^5=\frac{2^5}{3^5}\) |
| \(\displaystyle k^{a/b}=\sqrt[b]{k^a}\) |
\(\displaystyle 5^{2/3}=\sqrt[3]{5^2}\) |
| \(\displaystyle k^{-a}=\frac{1}{k^a}\) |
\(\displaystyle 3^{-2}=\frac{1}{3^2}=\frac{1}{9}\) |
| \(\displaystyle k^0=1\) |
\(\displaystyle 3^0=1\) |
Problems and Videos
Evaluate
\(\textbf{1)}\) \( \displaystyle 9^{3/2} \)
The answer is \( 27 \)
\(\textbf{2)}\) \( \displaystyle 8^{1/3} \)
The answer is \( 2 \)
\(\textbf{3)}\) \( \displaystyle 8^{2/3} \)
The answer is \( 4 \)
\(\textbf{4)}\) \( \displaystyle 8^{4/3} \)
The answer is \( 16 \)
\(\textbf{5)}\) \( \displaystyle 8^{5/3} \)
The answer is \( 32 \)
\(\textbf{6)}\) \( \displaystyle 4^{3/2} \)
The answer is \( 8 \)
\(\textbf{7)}\) \( \displaystyle 4^{5/2} \)
The answer is \( 32 \)
\(\textbf{8)}\) \( \displaystyle 16^{1/4} \)
The answer is \( 2 \)
\(\textbf{9)}\) \( \displaystyle 27^{1/3} \)
The answer is \( 3 \)
\(\textbf{10)}\) \( \displaystyle 27^{2/3} \)
The answer is \( 9 \)
\(\textbf{11)}\) \( \displaystyle 125^{2/3} \)
The answer is \( 25 \)
Challenge Problems
\(\textbf{12)}\) \( \displaystyle 16^{2/5} \)
The answer is \( 2 \sqrt[5]{8} \, \) or \( \, 2\cdot 2^{3/5} \)
\(\textbf{13)}\) \( (\displaystyle 4^{1/2})( \displaystyle4^{2/3}) \)
The answer is \( 4\sqrt[3]{2} \, \) or \( \, 4 \cdot 2^{1/3} \)
\(\textbf{14)}\) \( \displaystyle \left(\frac{4}{9}\right)^{-1/2} \)
The answer is \( \displaystyle \frac{3}{2} \)
\(\textbf{15)}\) \( \displaystyle \frac{1}{x^{2/3}} \)
The answer is \( \displaystyle \frac{\sqrt[3]{x}}{x} \, \) or \( \, \displaystyle \frac{x^{1/3}}{x} \)
\(\textbf{16)}\) \( \displaystyle \frac{2x^2+3x}{\sqrt[3]{x}} \)
The answer is \( \displaystyle \frac{2x^{8/3}+3x^{5/3}}{x} \)
\(\textbf{17)}\) \( \displaystyle \frac{zw}{\sqrt[3]{x}} \)
The answer is \( \displaystyle \frac{x^{2/3}zw}{x} \)
See Related Pages\(\)
