Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cup B\).

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap B\).

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(A\cap C\).

Let \(A=\{1, 3, 5\}\), \(B=\{0, 2, 4\}\), and \(C=\{1, 2, 3, \ldots\}\). Find \(B\cup C\).

For the set \(\left\{-5, \,-3.5, \,0, \,\frac{3}{4}, \,\sqrt{3}, \,\sqrt{5}, \,9\right\}\), list:

1. whole numbers

2. integers

3. rational numbers

4. irrational numbers

5. real numbers

Simplify \(\left(-3x^2\right)\left(5x^4\right)\) using the properties of exponents.

Simplify \(\left(-2x^2\right)^3\left(4x^5\right)\) using the properties of exponents.

Simplify \(\left(x^2\right)^4\left(x^2y^3\right)^2\left(y^4\right)^3\) using the properties of exponents.

Write \(5^{-2}\) with positive exponents, then simplify.

Write \((-2)^{-3}\) with positive exponents, then simplify.

Write \(\left(\displaystyle\frac{3}{4}\right)^{-2}\) with positive exponents, then simplify.

Apply property 6 to each expression, and then simplify the result. All answers that contain exponents should contain positive exponents only.

Simplify:

1. \(\left(2x^2y^4\right)^0\)

2. \(\left(2x^2y^4\right)^1\)

Simplify \(\displaystyle\frac{\left(x^3\right)^{-2}\left(x^4\right)^5}{\left(x^{-2}\right)^7}\)

Simplify \(\displaystyle\frac{6a^5b^{-6}}{12a^3b^{-9}}\)

Simplify \(\displaystyle\frac{\left(4x^{-5}y^3\right)^2}{\left(x^4y^{-6}\right)^{-3}}\)

Write \(376,000\) in scientific notation.

Write \(4.52 \times 10^3\) in expanded form.

Simplify each expression, and write all answers in scientific notation.

1. \(\left(2 \times 10^8\right)\left(3 \times 10^{-3}\right)\)

2. \(\displaystyle\frac{4.8 \times 10^9}{2.4 \times 10^{-3}}\)

3. \(\displaystyle\frac{\left(6.8\times 10^5\right)\left(3.9 \times 10^{-7}\right)}{7.8 \times 10^{-4}}\)

Identify \(6x^2+2x-1\) as a monomial, binomial, or trinomial if possible and give the degree.

Identify \(5x-3\) as a monomial, binomial, or trinomial if possible and give the degree.

Identify \(7x^6-5x^3+2x-4\) as a monomial, binomial, or trinomial if possible and give the degree.

Identify \(-7x^4\) as a monomial, binomial, or trinomial if possible and give the degree.

Identify \(15\) as a monomial, binomial, or trinomial if possible and give the degree.

Add \(5x^2-4x+2\) and \(3x^2+9x-6\)

Simplify \(4x-3[2-(3x+4)]\)

Find the value of \(5x^3-3x^2+4x-5\) when \(x\) is \(2\)

Find the product of \(4x^3\) and \(5x^2-3x+1\)

Multiply \(2x-3\) and \(x+5\)

Multiply \((2x-3y)\) and \(\left(3x^2-xy+4y^2\right)\) vertically.

Multiply: \((4a-5b)(3a+2b)\)

Multiply: \((3-2t)(4+7t)\)

Multiply \(\left(2x+\displaystyle\frac{1}{2}\right)\left(4x-\displaystyle\frac{1}{2}\right)\)

Multiply \(\left(a^5+3\right)\left(a^5-7\right)\)

Multiply: \((2x+3)(5y-4)\)

Find \((4x-6)^2\)

Expand \((x+7)^2\)

Expand \((3t-5)^2\)

Expand \((4x+2y)^2\)

Expand \(\left(5-a^3\right)^2\)

Multiply: \(\left(x+\dfrac{1}{3}\right)^2\)

Multiply \((3x-5)\) and \((3x+5)\)

Multiply: \((x-5)(x+5)\)

Multiply: \((2a-3)(2a+3)\)

Multiply \(\left(x^2+4\right)\left(x^2-4\right)\)

Multiply \(\left(x^3-2a\right)\left(x^3+2a\right)\)

Factor \(2x^5-8x^3\)

Factor \(\; 2x^5+8x^3\)

Factor \(3x^4-18x^3+27x^2\)

Factor \(6a^2-11a+4\)

Factor \(\;6a^2-11a-4\)

Factor \(2x^4+16x\)

Factor \(2ab^5+8ab^4+2ab^3\)

Factor \(4x^2-6x+2ax-3a\)

Factor \(\;4x^4-35x^2-9\)

Factor \(2x^2(x-3)-5x(x-3)-3(x-3)\)

Reduce \(\displaystyle\frac{x^2-9}{x-3}\)

Reduce \(\displaystyle\frac{y^2-5y-6}{y^2-1}\)

Reduce \(\displaystyle\frac{2a^3-16}{4a^2-12a+8}\)

Reduce \(\displaystyle\frac{a-b}{b-a}\)

Multiply \(\displaystyle\frac{6}{7}\cdot \displaystyle\frac{14}{18}\)

Multiply \(\displaystyle\frac{8x^3}{27y^8}\cdot \displaystyle\frac{9y^3}{12x^2}\)

Multiply \(\displaystyle\frac{2y^2-4y}{2y^2-2}\cdot \displaystyle\frac{y^2-2y-3}{y^2-5y+6}\)

Divide \(\displaystyle\frac{x^2-y^2}{x^2-2xy+y^2}\div \displaystyle\frac{x^3+y^3}{x^3-x^2y}\)

Multiply \(\left(4x^2-36\right)\cdot \displaystyle\frac{12}{4x+12}\)

Multiply \(3(x-2)(x-1)\cdot \displaystyle\frac{5}{x^2 -3x+2}\)

Add \(\displaystyle\frac{x}{x^2-1}+\displaystyle\frac{1}{x^2-1}\)

Add \(\displaystyle\frac{3}{14}+\displaystyle\frac{7}{30}\)

Add \(\displaystyle\frac{-2}{x^2-2x-3}+\displaystyle\frac{3}{x^2-9}\)

Subtract \(\displaystyle\frac{x+4}{2x+10}-\displaystyle\frac{5}{x^2-25}\)

Simplify: \(\displaystyle\frac{\displaystyle\frac{1}{x}+\displaystyle\frac{1}{y}}{\displaystyle\frac{1}{x}-\displaystyle\frac{1}{y}}\)

Simplify \(\displaystyle\frac{1-\displaystyle\frac{4}{x^2}}{1-\displaystyle\frac{1}{x}-\displaystyle\frac{6}{x^2}}\)

What are the two square roots of \(64\)?

Simplify if possible: \(\sqrt[3]{-8}\)

Simplify if possible: \(\sqrt{-4}\)

Simplify if possible: \(-\sqrt{25}\)

Simplify if possible: \(\sqrt[5]{-32}\)

Simplify if possible: \(\sqrt[4]{-81}\)

Simplify as much as possible: \(\sqrt{25a^4b^6}\)

Simplify as much as possible: \(\sqrt[3]{x^6y^{12}}\)

Simplify as much as possible: \(\sqrt[4]{81r^8s^{20}}\)

Write as a root, then simplify: \(8^{\frac{1}{3}}\)

Write as root, then simplify: \(36^{\frac{1}{2}}\)

Write as a root, then simplify: \(-25^{\frac{1}{2}}\)

Write as a root, then simplify: \((-25)^{\frac{1}{2}}\)

Write as a root, then simplify: \(\left(\dfrac{4}{9}\right)^{\frac{1}{2}}\)

Write as a rational exponent and simplify: \(\sqrt[3]{x^6y^{12}}\)

Write as a rational exponent and simplify: \(\sqrt[4]{81r^8s^{20}}\)

Simplify as much as possible: \(8^{\frac{2}{3}}\)

Simplify as much as possible: \(9^{-\frac{3}{2}}\)

Simplify as much as possible: \(\left(\dfrac{27}{8}\right)^{-\frac{4}{3}}\)

Simplify as much as possible: \(x^{\frac{1}{3}}\cdot x^{\frac{5}{6}}\)

Simplify as much as possible: \(\left(y^{\frac{2}{3}}\right)^{\frac{3}{4}}\)

Simplify as much as possible: \(\dfrac{z^{\frac{1}{3}}}{z^{\frac{1}{4}}}\)

Write \(\sqrt{50}\) in simplified form.

Write in simplified form: \(\sqrt{48x^4y^3}\), where \(x\), \(y\geq0\).

Write \(\sqrt[3]{40a^5b^4}\) in simplified form.

Simplify \(\sqrt{\displaystyle\frac{5}{6}}\)

Rationalize the denominator in \(\displaystyle\frac{4}{\sqrt{3}}\)

Rationalize the denominator in \(\displaystyle\frac{7}{\sqrt[3]{4}}\)

Simplify, but do not assume the variable represents a positive number. \[\sqrt{9x^2}\]

Simplify, but do not assume the variable represents a positive number. \[\sqrt{x^2-6x+9}\]

Simplify, but do not assume the variable represents a positive number. \[\sqrt{x^3-5x^2}\]

Combine \(5\sqrt{3}-4\sqrt{3}+6\sqrt{3}\)

Combine \(3\sqrt{8}+5\sqrt{18}\)

Multiply \(\left(3\sqrt{5}\right)\left(2\sqrt{7}\right)\)

Multiply \(\sqrt{3}\left(2\sqrt{6}-5\sqrt{12}\right)\)

Multiply \(\left(\sqrt{3}+\sqrt{5}\right)\left(4\sqrt{3}-\sqrt{5}\right)\)

Expand and simplify: \(\left(\sqrt{x}+3\right)^2\)

Multiply \(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{6}-\sqrt{2}\right)\)

Divide \(\displaystyle\frac{6}{\sqrt{5}-\sqrt{3}}\) (Rationalize the denominator)

Write in terms of \(i\): \(\sqrt{-25}\)

Write in terms of \(i\): \(\sqrt{-49}\)

Write in terms of \(i\): \(\sqrt{-12}\)

Write in terms of \(i\): \(\sqrt{-17}\)

Simplify as much as possible: \(i^{30}\)

Simplify as much as possible: \(i^{11}\)

Simplify as much as possible: \(i^{40}\)

Find \(x\) and \(y\) if \(3x+4i=12-8yi\)

Find \(x\) and \(y\) if \((4x-3)+7i=5+(2y-1)i\)

Simplify: \((3+4i)+(7-6i)\)

Simplify: \((7+3i)-(5+6i)\)

Simplify \((5-2i)-(9-4i)\)

Multiply: \((3-4i)(2+5i)\)

Multiply: \(2i(4-6i)\)

Expand: \((3+5i)^2\)

Multiply: \((2-3i)(2+3i)\)

Divide: \(\dfrac{2+i}{3-2i}\)