Landscaping Costs and Earnings Analysis

The video tutorial covers four math problems. Problem 20 involves simplifying expressions with negative exponents by rewriting them with positive exponents and combining bases. Problem 21 demonstrates proving the equality of sums in a grid using algebraic equations. Problem 22 deals with solving a sales tax problem by setting up and solving equations. Problem 23 calculates the earnings of a craftsperson after a store takes a percentage of sales and a fixed amount per item.

What is the simplified form of the expression 5^-8 * 7^-9?

• 1 / (5^8 * 7^9)

• 35^8 * 7

• 5^8 * 7^9

• 1 / (35^8 * 7)

In a 3x3 grid, if the middle number is x, what is the sum of the numbers in the vertical rectangle?

• x + 5 + x - 5

• x + 1 + x + x - 1

• x - 5 + x + x + 5

• 3x

How can you prove that the sum of numbers in the vertical rectangle equals the sum in the horizontal rectangle in a 3x3 grid?

• By adding 5 to each number

• By subtracting 1 from each number

• By multiplying each number by 2

• By showing 3x = 3x

If a landscaper pays $315 after a 5% sales tax, what is the equation representing the pretax cost?

• 1.05px = 315

• px = 315

• 0.95px = 315

• px + 6 = 315

Without sales tax, how many more blocks could the landscaper buy for $315?

• 8 more blocks

• 7 more blocks

• 6 more blocks

• 5 more blocks

What is the equation that represents the situation where the landscaper could buy more blocks without tax?

• px = 315

• p(x + 6) = 315

• 1.05px = 315

• px - 6 = 315

How much does a craftsperson earn if the store takes $3 and 40% of the sale price?

• p - 3 - 0.4p

• p - 3

• 0.6p - 3

• p - 0.4p

If the sale price is represented by p, what fraction represents the craftsperson's earnings?

• 4/5p - 3

• 2/5p - 3

• 3/5p - 3

• 1/2p - 3

What percentage of the sale price does the store take in addition to $3?

• 30%

• 40%

• 50%

• 60%

What is the minimum sale price for items sold in the store?

• $3

• $4

• $5

• $6