# Factor the Expression (Answer)

Find the value of

(Hint: Use your algebra skills to factor the expression.)

Answer ?

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# Exponents Problem Set (Answer)

**Problem set.**

1. A population of squirrels triples each year. If there are 50 squirrels now, how many will there be 5 years from now?

2. Alannah puts $0.01 into a bank account which will double her money each day. She needs $20.00 to buy a toy. How many days will it take until she has enough money?

3. Britney Gallivan was the rst person to fold a piece of paper in half 12 times,

something which had previously been believed to be impossible. How many layers of paper would be in that stack?

4. Ramone dumped a large bucket of water onto his driveway to rinse it o. The water from the bucket covered twice as much area every 2 seconds after it initially hit the ground. After 20 seconds, the whole driveway was covered.

How long did it take the water to cover half of the driveway?

# Opening Exponents Problem

**Math Problem**

My rich uncle gave me a dollar for my 3rd birthday. On each birthday after that, he tripled his previous gift. How much money did I receive from my uncle on my 8th birthday?

Solution

Each year the gift my uncle gives me triples, which means the new gift is found by multiplying the previous year’s gift by 3. So, on my 4th birthday my uncle gave me 1 x 3 = 3 dollars, on my 5th birthday he gave me 1x3x3 = 3×3 dollars, and so on.

Therefore, on my 8th birthday he gave me 3 x 3 x 3 x 3 x 3 = 243 dollars. An easier way to write this is using a **power: 3^5 = 243**.

# Definition of Least Common Multiple (LCM)

**Definition:**

A multiple of a number is the product of the number and another whole number. Factors and multiples are closely related.

For example, 9 is a factor of 90, so 90 is a multiple of 9.

**Denition: **

The least common multiple or lcm of two or more numbers is the lowest number that is a multiple of each of the numbers. One method of nding the least common multiple involves listing the multiples of each number until you nd the rst number that is a multiple of both.

**Example Find the least common multiple of 6 and 8.**

The first few multiples of 6 are 6 12 18 24 30 36 42 48…

The first few multiples of 8 are 8 16 24 32 40 48 56 64…

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# GCD: Problem Set and Answer

**Math Problem Set**

1. Sam was buying hot dogs and hot dog buns for a backyard barbeque. Hot Dogs come in packs of 16, but buns come in packs of 12. How many packs of each will Sam have to buy so that there are no hot dogs or buns left over?

2. A florist has 72 roses, 84 tulips and 48 orchids that she wants to use to create bouquets. What is the largest number of identical bouquets she can put together without having any owers left over?

3. Three alarm clocks are set o at the same time. If the rst one beeps every 9

seconds, the second one beeps every 12 seconds and the third one beeps every 15 seconds, how long will it be until they beep at the same time?

4. Vince has three pieces of rope with lengths of 300 cm, 312 cm and 396 cm. He wants to cut the three pieces of rope into smaller pieces of equal length with none left over.

(a) What is the greatest possible length of each of the smaller pieces of rope?

(b) How many of the smaller pieces of rope will he have altogether?

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