8th Grade Unit 1

Rules of Exponents

100

Simply the following - x³x⁵

x⁸

200

Explain why x⁰ is always true.

A number raised to the power of 1 is itself, that number divided by itself will always be one. When a number raised to 1 is divided by itself the exponent decreases to 0 because of the quotient rule.

300

Simplify: (p³p^-6)²

p^-6

Writing Scientific Notation

100

Write this number in scientific notation: 0.0000571

5.71x 10^-5

200

Write this number in standard form: 4.23 x 106

4,230,000

300

Explain what is actually happening when we “move the decimal”.

You are indicating that we are multiplying or dividing by powers of 10 because all the digits remain the same but the number is 10 times more or 10 times less.

Estimating with Scientific Notation

100

Approximate: (5.3 x 10²) x (1.1 x 10³). Provide your answer in correct scientific notation. Simplify.

5 x 10⁵

200

Approximate: (6.8 x 10⁵) / (2.03 x 10³). Provide your answer in correct scientific notation. Simplify.

3.5 x 10²

300

The distance from the Earth to the Sun is 1.5 x 10¹¹ meters. The speed of light is 3 x 10⁸ meters per second. Estimate how long it will take for light to go from the Sun to Earth. Provide your answer in correct scientific notation. Simplify.

5 x 10²

Performing Operations with Scientific Notation

100

Calculate: (2.2 x 10⁵) x (1 x 10³). Provide your answer in correct scientific notation. Simplify.

2.2 x 10⁸

200

Calculate: (3.157 x 10⁶) / (2.4 x 10³). Provide your answer in correct scientific notation. Simplify.

1.32 x 10³

300

Calculate: (2.5 x 10⁹) x (6.4 x 10²). Provide your answer in correct scientific notation. Simplify.

1.6 x 10¹²