5.5 Homework: fractional exponents

$100^{\left(\frac{1}{2}\right)}$

$100^{-2}$

$100^{\left(\frac{-1}{2}\right)}$

$100^{\left(\frac{3}{2}\right)}$

$100^{\left(\frac{-3}{2}\right)}$

Check all of your answers above on your calculator. If any of them did not come out right, figure out what went wrong, and fix it!

Solve for $x$ : $\frac{x^{}}{x^{}}17^{\left(\frac{1}{2}\right)}$ $17^{\left(\frac{1}{2}\right)}$

Solve for $x$ : $x^{\left(\frac{1}{2}\right)}=9$

Simplify: $\frac{x}{\sqrt{x}}$

Simplify: $\frac{x^{}+\sqrt{x}}{x^{}+\frac{1}{\sqrt{x}}}$

$x^3$

• a Find the inverse function.
• b Test it.

$x^{-2}$

• a Find the inverse function.
• b Test it.

$x^0$

• a Find the inverse function.
• b Test it.

Can you find a generalization about the inverse function of an exponent?

Graph $y=2^x$ by plotting points. Make sure to include both positive and negative $x$ values.

Graph $y=22^x$ by doubling all the y-values in the graph of $y=2^x$ .

Graph $y=2^x+1$ by taking the graph $y=2^x$ and “shifting” it to the left by one.

Graph $y=\left(\frac{1}{2}\right)^x$ by plotting points. Make sure to include both positive and negative $x$ values.