Simplify

1. \(4^3\)

2. \(-3^4\)

3. \((-2)^5\)

4. \(\left(-\displaystyle\frac{3}{4}\right)^2\)

Simplify

1. \(5^3 \cdot 5^6\)

2. \(x^7 \cdot x^8\)

3. \(3^4 \cdot 3^8 \cdot 3^5\)

Simplify

1. \(\left(4^5\right)^6\)

2. \(\left(x^3\right)^5\)

Simplify \(\left(-\displaystyle\frac{1}{4}x^2y^3\right)^2\)

Simplify \(\left(x^4\right)^3\left(x^2\right)^5\)

Simplify \((2y)^3(3y^2)\)

Simplify \(\left(2x^2y^5\right)^3\left(3x^4y\right)^2\)

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

Write \(4,758,000\) in scientific notation.

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

Simplify

1. \(2^{-3}\)

2. \(5^{-2}\)

3. \(3x^{-6}\)

4. \((4x)^{-3}\)

Simplify

1. \(\displaystyle\frac{x^9}{x^6}\)

2. \(\displaystyle\frac{x^4}{x^{10}}\)

3. \(\displaystyle\frac{2^{15}}{2^{20}}\)

Simplify

1. \(\left(\displaystyle\frac{x}{2}\right)^3\)

2. \(\left(\displaystyle\frac{5}{y}\right)^2\)

3. \(\left(\displaystyle\frac{2}{3}\right)^4\)

Simplify

1. \(8^0\)

2. \(8^1\)

3. \(4^0+4^1\)

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

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

Simplify \(\displaystyle\frac{x^{-8}}{\left(x^2\right)^3}\)

Simplify \(\left(\displaystyle\frac{y^5}{y^3}\right)^2\)

Simplify \(\left(3x^5\right)^{-2}\)

Simplify \(\; x^{-8} \cdot x^5\)

Simplify \(\displaystyle\frac{\left(a^3\right)^2a^{-4}}{\left(a^{-4}\right)^3}\)

One square is larger than another. If the side of the larger square is \(3\) times as long as the side of the smaller square, how many of the smaller squares will fit inside the larger square?

You have two cubes. If the side of one cube is \(3\) times the side of the other cube, how many of the smaller cubes will fit inside the larger cube?

Write \(0.000584\) in scientific notation.

Multiply.

1. \(\left(-3x^2\right)\left(4x^3\right)\)

2. \(\left(\dfrac{4}{5}x^5\cdot y^2\right)\left(10x^3\cdot y\right)\)

Divide

1. \(\displaystyle\frac{15x^3}{3x^2}\)

2. \(\displaystyle\frac{39x^2y^3}{3xy^5}\)

Divide \(25a^5b^3\) by \(50a^2b^7\).

Multiply \(\left(4 \times 10^7\right)\left(2 \times 10^{-4}\right)\)

Divide \(\displaystyle\frac{9.6 \times 10^{12}}{3\times 10^4}\)

Combine the following monomials.

1. \(-3x^2+15x^2\)

2. \(9x^2y-20x^2y\)

3. \(5x^2+8y^2\)

Apply the distributive property and simplify.

1. \(x^2\left(1-\dfrac{1}{x}\right)\)

2. \(ab\left(\dfrac{1}{b}-\dfrac{1}{a}\right)\)

Simplify \(\displaystyle\frac{\left(6x^4y\right)\left(3x^7y^5\right)}{9x^5y^2}\)

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

Simplify \(\displaystyle\frac{14x^5}{2x^2}+\displaystyle\frac{15x^8}{3x^5}\)

Add \(\left(2x^2-5x+3\right)+\left(4x^2+7x-8\right)\)

Add \(x^2+3x+2x+6\)

Subtract \(\left(3x^2+x+4\right)-\left(x^2+2x+3\right)\)

Subtract \(-4x^2+5x-7\) from \(x^2-x-1\)

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

Find the value of \(2x^2+3x+5\) when \(x=3\)

Multiply \(\,3x^2\left(2x^2+4x+5\right)\)

Multiply \((3x-5)(2x-1)\)

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

Multiply \((2x+3)(3x^2-2x+1)\)

Multiply.

1. \(4a^2\left(2a^2-3a+5\right)\)

2. \((x-2)(y+3)\)

3. \((x+y)(a-b)\)

4. \((5x-1)(2x+6)\)

Multiply: \((3x-2)^2\)

Multiply: \((3x-1)(3x+1)\)

The length of a rectangle is \(3\) more than twice the width. Write an expression for the area.

A store selling flash drives for computers knows from past experience that it can sell \(x\) flash drives each day at a price of \(p\) dollars each, according to the equation \(x=800-100p\). Write a formula for the daily revenue.