5.1 Homework Problems: Exponents
1. Simplify the following exponential expressions with positive exponents only
a. 83 * 80
b. 32 * 3
c. 3-1
d. 5-2
e. (-2)4 (-2)0
f. 3(2-3)
g. x2 * x3
h. 2x-1
i. [latex]\frac{10^3}{10^4}[/latex]
j. [latex]\frac{x^{-2}}{x^2}[/latex]
k. (3y) (y4)
l. (4x3)(9x1)
m. [latex]\frac{-10x^5}{2x}[/latex]
n. [latex]\frac{{10}^4\ \bullet\ {10}^3}{{10}^{-2}}[/latex]
o. (-3xy)(-5x2y-3)
p. [latex]\frac{-8x^2y^4}{4x^3y^2}[/latex]
2. Use the rules for raising exponents to a power to simplify the expressions with positive exponents only
a. [latex]4\left(-3x^2\right)^3[/latex]
b. [latex]5\left(x^2y^{-1}\right)[/latex]
c. [latex]-2\left(3x^5y^{-2}\right)^{-3}[/latex]
d. [latex]{\ \left(\frac{-4x}{y^2}\right)}^2[/latex]
e. [latex]\left(\frac{-7^2x^2y}{y^3}\right)^{-1}[/latex]
f. [latex]{ \ \left(\frac{3xy^3}{4x^2y^{-3}}\right)}^{-1}\left(\frac{2x^3y^{-1}}{9x^{-3}y^{-1}}\right)^2[/latex]
3. Perform the indicated operation and write each of the resulting numbers in scientific notation
a. [latex]\ 0.0003\times0.0000025[/latex]
b. [latex]300\times0.00015[/latex]
c. [latex]\frac{3900}{0.003}[/latex]
d. [latex]\frac{0.005\times650\times3.3}{0.0011\times2500}[/latex]