Express the following as a power of the indicated bases:
a. 729 as a power of 3.
b. 128 as a power of 2.
c. [latex] (9)^{\frac{3}{2}} [/latex] as a power of 3.
d. [latex] (16)^{\frac{3}{4}} [/latex] as a power of 2.
Express the following as a single power:
a. [latex] 3^4 \times 3^{(4 + 2)} [/latex]
b. [latex] 10^4 \times 10^{(3 + 2)} [/latex]
Simplify using the laws of exponents and then evaluate, rounding to two decimal places, wherever applicable.
a. [latex] \displaystyle{\frac{2^3 \times (3)^3 \times 3^4}{2^3 \times (2^3)^2 \times 3^5}} [/latex]
b. [latex] \displaystyle{\frac{2^4 \times (3^2)^4 \times 2^2}{2^5 \times (3^3)^2 \times 2^0}} [/latex]
Evaluate Problems 4 to 12. Round to two decimal places, wherever applicable.
a. [latex] (2^2 \times 3^3 \times 5^0)^{-1} [/latex]
b. [latex] (3^2 \times 2^{-2} \times 5)^0 [/latex]
a. [latex] \displaystyle{\left(\frac{3}{2}\right)^2 \times \frac{3}{8}} [/latex]
b. [latex] \displaystyle{4 \times \frac{8}{5} \div \frac{4}{3} + \sqrt{4} - 1} [/latex]
a. [latex] \displaystyle{\frac{2}{5} \times \sqrt{100} + 2^4 \div \frac{5}{3}} [/latex]
b. [latex] \displaystyle{\sqrt{36} \times \frac{4}{3} \div \frac{8}{6} - 7 + 2} [/latex]
a. [latex] \displaystyle{\left(\frac{2}{3} + \frac{4}{3}\right)^5} [/latex]
b. [latex] \displaystyle{\left(\frac{9^{\frac{2}{5}}}{9^{\frac{3}{5}}}\right) \times 3^2} [/latex]
a. [latex] -5^3(-25)^3 [/latex]
b. [latex] 3^{-2} \times 3^3 [/latex]
a. [latex] (-3)^3 - (-1)^3 [/latex]
b. [latex] (-2)^5 \times (4 - 5)^3 - (-10) [/latex]
a. [latex] (-5)^3 - (-4)^3 [/latex]
b. [latex] (-4)^5 \div (-2)^6 [/latex]
a. [latex] -9 + |(-4) \div (-2)| [/latex]
b. [latex] |12 - 8 \times 2| - |-4| [/latex]
a. [latex] \displaystyle{\frac{16^{\frac{1}{2}} \times 6}{81^{\frac{1}{2}}}} [/latex]
b. [latex] \displaystyle{\frac{9^{\frac{1}{2}} \times 81^{\frac{1}{2}}}{13^2 - 5^2}} [/latex]
Write the numbers in scientific notation:
a. [latex] 10.09 [/latex]
b. [latex] 0.005 [/latex]
c. [latex] 60,200 [/latex]
Write the numbers in standard form:
a. [latex] 2.7 \times 10^3 [/latex]
b. [latex] 4.15 \times 10^{-3} [/latex]
c. [latex] 3.0405 \times 10^{-2} [/latex]
For Problems 15 and 16, perform the arithmetic operations and express the answers in scientific notation. Do not round the answers.
a. [latex] 4.01 \times 10^4 + 9.99 \times 10^3 [/latex]
b. [latex] 4.06 \times 10^{-8} - 9.94 \times 10^{-7} [/latex]
a. [latex] (6.50 \times 10^7) \times (8.0 \times 10^{-9}) [/latex]
b. [latex] (1.225 \times 10^{14}) \div (8.75 \times 10^{-6}) [/latex]