Calculate the difference between [latex] 2^5 [/latex] and [latex] 5^2 [/latex].
Calculate the difference between [latex] 3^4 [/latex] and [latex] 4^3 [/latex].
Express 243 as a power of 3 and then evaluate [latex] \displaystyle{243\frac{3}{5}} [/latex].
Express 512 as a power of 2 and then evaluate [latex] \displaystyle{512\frac{4}{9}} [/latex].
Express Problems 5 to 8 as a single power and then evaluate.
a. [latex] \displaystyle{(2^6)^{\frac{1}{3}}} [/latex] b. [latex] \displaystyle{(5^{15})^{\frac{1}{5}}} [/latex]
a. [latex] \displaystyle{\left(\frac{3^9}{3^3}\right)^{\frac{1}{3}}} [/latex] b. [latex] \displaystyle{\left(\frac{2^{12}}{2^4}\right)^{\frac{1}{4}}} [/latex]
a. [latex] \displaystyle{(3^2)^{\frac{1}{2}} \times (3^3)^{\frac{2}{3}}} [/latex] b. [latex] \displaystyle{(6^2)^{\frac{1}{3}} \times (6^3)^{\frac{1}{9}}} [/latex]
a. [latex] \displaystyle{(2^2)^{\frac{1}{4}} \times (2^5)^{\frac{3}{10}}} [/latex] b. [latex] \displaystyle{(5^3)^{\frac{2}{3}} \times (5^2)^{\frac{1}{2}}} [/latex]
For Problems 9 to 16, simplify using laws of exponents and then evaluate.
a. [latex] \displaystyle{\frac{2^3 \times 3^4 \times 2^2}{3 \times 2^5}} [/latex] b. [latex] \displaystyle{\frac{(5^2) \times 5^4}{5^7}} [/latex]
a. [latex] \displaystyle{\frac{5^2 \times 7^3 \times 54}{7 \times 5^6}} [/latex] b. [latex] \displaystyle{\frac{(2^5) \times 2^2}{2^{17}}} [/latex]
a. [latex] (-5)^2 \times (4)^2 [/latex] b. [latex] -10^4 \times 10^3 [/latex]
a. [latex] (-2)^2 \times (3)^2 [/latex] b. [latex] -2^4 \times 2^2 [/latex]
a. [latex] \displaystyle{(125)^{-\frac{1}{3}}} [/latex] b. [latex] \displaystyle{(49)^{-\frac{1}{2}}} [/latex] c. [latex] \displaystyle{\sqrt{\frac{64}{81}}} [/latex]
a. [latex] \displaystyle{(16)^{-\frac{1}{4}}} [/latex] b. [latex] \displaystyle{(27)^{-\frac{1}{3}}} [/latex] c. [latex] \displaystyle{\sqrt{\frac{25}{49}}} [/latex]
a. [latex] \displaystyle{\sqrt{7^4}} [/latex] b. [latex] \displaystyle{\sqrt{\frac{25}{36}}} [/latex] c. [latex] \displaystyle{\sqrt[3]{\frac{216}{125}}} [/latex]
a. [latex] \displaystyle{\sqrt{5^6}} [/latex] b. [latex] \displaystyle{\sqrt{\frac{49}{64}}} [/latex] c. [latex] \displaystyle{\sqrt[3]{\frac{64}{27}}} [/latex]
Evaluate Problems 17 to 32 and express the answers rounded to two decimal places, wherever applicable.
a. [latex] \displaystyle{\frac{16 + 4(-3)}{10 - 4 + 1} + \frac{(16 + 4) - 3}{10 - (4 + 1)}-} [/latex]
b. [latex] 14- 3 [(6 - 9)(-4) + 12] \div (-2) [/latex]
a. [latex] \displaystyle{\frac{2(-6) + 4}{24 - (7 + 3)} + \frac{2(-6 + 4)}{24 - 7 + 3}-} [/latex]
b. [latex] 5(-4) -3[(- 9 + 6) + (-3) - 4] [/latex]
a. [latex] [(1 + 12)(1 - 5)]^2 \div [(5 + 3) \times 2^2 - (-2)^2] [/latex]
b. [latex] 2^2[(9 - 7) \div 2 + 9 - 4] [/latex]
a. [latex] 8 \div 4 + (4 - 6^2) \div (13 - 5) \times (-2)^6 [/latex]
b. [latex] 6 \div [4 \times (2 - 8) \div (3^2 + 3)] \div 4 [/latex]
a. [latex] 64 \div (-2)^4 + 4 (-3^2) \div 2 - 5 [/latex]
b. [latex] (-6)^2 - 9^2 \div 3^3 - (-3)(-2) [/latex]
a. [latex] 8 \div (-2)^3(-9) + 6(-5)^3 \div (-5)^2 [/latex]
b. [latex] (-8)^2 - 4^3 \div 2^2 - (-6)(-2) [/latex]
a. [latex]\displaystyle{6,000\left(1 + \frac{0.06}{12}\right)^{36}} [/latex]
b. [latex] 2,000(1 + 0.004)^{-24} [/latex]
a. [latex]\displaystyle{4,000\left(1 + \frac{0.075}{12}\right)^{60}} [/latex]
b. [latex] 5,000(1 + 0.003)^{-48} [/latex]
[latex]\displaystyle{\frac{3,000[(1.06)^{25} - 1]}{0.06}} [/latex]
[latex]\displaystyle{\frac{1,400[(1.03)^{30} - 1]}{0.03}} [/latex]
[latex]\displaystyle{\frac{950[1 - (1.03)^{15}]}{0.03}} [/latex]
[latex]\displaystyle{\frac{1,200[1 - (1.04)^{20}]}{0.04}} [/latex]
a. [latex] -15 - (-15) [/latex]
b. [latex] -14 - (-7) [/latex]
a. [latex] 13 - (-11) + 0 [/latex]
b. [latex] 22 - (-4) - 6 [/latex]
a. [latex] 8 + |2 - 7| [/latex]
b. [latex] -|-23| - |10 - 15| [/latex]
a. [latex] 15 - |3 - 9| [/latex]
b. [latex] -|-42| - |35 - 18| [/latex]
Determine the number of significant digits in each of the following numbers and write them in scientific notation:
a. [latex] 7,101.1 [/latex]
b. [latex] 54.001 [/latex]
c. [latex] 0.0072 [/latex]
Determine the number of significant digits in each of the following numbers and write them in scientific notation:
a. [latex] 54,020 [/latex]
b. [latex] 0.2055 [/latex]
c. [latex] 0.09081 [/latex]
Write the numbers in standard form.
a. [latex] 8.9 \times 10^2 [/latex]
b. [latex] 5.6 \times 10^{-2} [/latex]
c. [latex] 9.64 \times 10^{-4} [/latex]
Write the numbers in standard form.
a. [latex] 5.1 \times 10^3 [/latex]
b. [latex] 6.8 \times 10^{-4} [/latex]
c. [latex] 4.75 \times 10^{-4} [/latex]
For Problems 37 to 44, perform the arithmetic operations and write the answers in scientific notation. Do not round the answer.
a. [latex] 4.65 \times 10^{14} + 9.95 \times 10^{12} [/latex]
b. [latex] 7.02 \times 10^{-2} + 6.95 \times 10^{-3} [/latex]
a. [latex] 7.28 \times 10^6 + 4.35 \times 10^5 [/latex]
b. [latex] 1.64 \times 10^{-12} + 5.5 \times 10^{-10} [/latex]
a. [latex] 4.01 \times 10^6 - 3.56 \times 10^4 [/latex]
b. [latex] 3.56 \times 10^{-3} - 8.01 \times 10^{-4} [/latex]
a. [latex] 1.25 \times 10^7 - 9.75 \times 10^5 [/latex]
b. [latex] 2.85 \times 10^{-1} - 7.45 \times 10^{-3} [/latex]
a. [latex] (6.0 \times 10^4) \times (4.0 \times 10^7) [/latex]
b. [latex] (7.5 \times 10^{-6}) \times (6.0 \times 10^{-5}) [/latex]
a. [latex] (7.75 \times 10^6) \times (2.0 \times 10^8) [/latex]
b. [latex] (9.45 \times 10^{-5}) \times (3.0 \times 10^{-7}) [/latex]
a. [latex] (2.0 \times 10^5) \div (4.0 \times 10^8) [/latex]
b. [latex] (1.45 \times 10^{-9}) \div (5.8 \times 10^{-3}) [/latex]
a. [latex] (1.75 \times 10^4) \div (3.50 \times 10^{-6}) [/latex]
b. [latex] (1.61 \times 10^{-7}) \div (4.83 \times 10^{-2}) [/latex]