Powers of Ten and Similar Triangles

This video tutorial covers negative exponents and powers of ten, focusing on writing expressions with single exponents, identifying equivalent expressions, and matching equations to real-world situations. It also explains the concept of similar triangles and finding missing side lengths. The tutorial is designed for 8th-grade students and includes practical examples and problem-solving techniques.

What is the result of multiplying one-tenth by itself three times, expressed as a power of ten?

• 10 to the power of -1

• 10 to the power of 1

• 10 to the power of -3

• 10 to the power of 3

How can you simplify the expression 10^4 * 10^-1?

• 10^5

• 10^3

• 10^-3

• 10^0

How do you express 10^5 divided by 10^7 as a single power of ten?

• 10^12

• 10^-2

• 10^2

• 10^-12

What is the result of 10^-3 * 10^2?

• 10^5

• 10^-5

• 10^1

• 10^-1

Which of the following is equivalent to 1/10,000?

• 10^-2

• 10^-4

• 10^4

• 10^2

In the equation y = 3x, what does the constant of proportionality represent?

• The total amount of mixture

• The number of cups of water per cup of salt

• The number of cups of salt

• The number of cups of water

If a store sells 4 hats for $10, what is the cost of one hat?

• $2.50

• $4.00

• $10.00

• $5.00

Which situation matches the equation y = 3.5x?

• A store sells 4 hats for $10

• A dump truck hauls 3.5 square feet of dirt per load

• A mixture has 3 cups of water for every cup of salt

• For every 48 cookies baked, 24 are given away

Why are triangles ABC and EDC similar?

• They have the same side lengths

• They have two pairs of congruent angles

• They are both right triangles

• They have the same area

What is the scale factor between triangles ABC and EDC if side BC is 24 units and side CD is 36 units?

• 0.5

• 1.0

• 1.5

• 2.0