Exponent Rules and Scientific Notation

Product of Powers

100

Finish the statement: a^m * aⁿ = ??

What is a^{(m + n)} ?

200

Simplify the product: 4r⁷ * 2r^-3 = ??

What is 8r⁴

300

Simplify the Expression. (1/2)² * (1/2)⁸ * (1/2)⁴ = ??

What is (1/2)¹⁴

400

Rewrite the expression using only positive exponents: d²y^-3 

What is d^{2 /} y³

500

Rewrite  1/s^-3 using a positive exponent

What is s³

Quotient of Powers

100

Complete the Statement: a^m / aⁿ = ??

What is a^{(m - n)}

200

Simplify the Expression: 3⁵ / 3² = ??

What is 3³

300

Reduce or Simplify: y² / y⁴ = ??

What is 1 / (y²) or y^-2

400

Apply the quotient rule and express your answer using positive exponents: x⁵y^-2 / x³y⁵

What is x² / y⁷

500

Reduce and Simplify. Use only positive exponents in your answer: 2w³x⁴ / 8w^-2x⁶

What is w⁵ / 4x²

Powers of Ten

100

Finish the statement: When writing numbers using a power of ten, the exponent tells you how many __________________________________.

What is A. how many times to multiply ten to itself. B. how many places to slide the decimal point right or left.

200

Write the number using a power of ten: 10,000,000,000,000,000.0 = ??

What is 10¹⁶

300

Write the number using a power of ten: 0.00000000000000000000000000000000001

What is 10^-35

400

10⁵⁰ * 10³ = ??

What is 10⁵³

500

There are 100 centimeters in one meter, and there are 10 millimeters in one centimeter. How many millimeters are there in one meter? 

What is 10² * 10¹ = 10³ millimeters in one meter or 1,000 millimeters 

Scientific Notation

100

Numbers in scientific notation can be written in expanded form and ____________ form.

What is standard form

200

When writing numbers in scientific notation, the absolute value of the factor out front must be between _______ and ________.

What is one and ten.

300

Write the number in standard form: 5.8 x 10⁷

What is 58,000,000.0

400

Write the number in scientific notation: 0.0000000000324 = ??

What is 3.24 x 10^-11

500

Write the number in scientific notation: 965,432,000,000,000 miles =

What is 9.65432 x 10¹⁴

Calculations in Scientific Notation

100

Complete the statement using < , > , or =. 

(6.4 x 10⁵) ____ (3.9 x 10⁷)

What is < (less than)

200

Perform the operation. Express your answer in scientific notation and standard form. 

(9.0 x 10^-2) * (4.0 x 10⁷) = ??

What is (3.6 x 10⁶) = 0.0000036

300

Perform the Calculation. Write you answer in scientific notation and standard form. (2.4 x 10⁵) / (2.0 x 10^-3) = ??

What is (1.2 x 10⁸) = 120,000,000.0

400

(4.5 x 10³)(2 x 10⁶)

What is 9 x 10⁹

500

The speed of light is approximately (6.71×10⁸) miles per hour. Approximately how for does light travel in 4 hours? Express your answer in standard form.

What is 2,684,000,000 miles