Q2 - What is an exponent?

 WHAT IS AN EXPONENT?

By: Sir Pj

An exponent is a shorthand way of writing a number multiplied by itself several times. It's like a little booster rocket strapped to a number, making it zoom to much bigger values!

Here's how it works:

• Base: This is the number you're multiplying. Think of it as the rocket itself.
• Exponent: This is a small number written above and to the right of the base. It tells you how many times to multiply the base by itself. Think of it as the number of boosters on the rocket.

For example, let's look at 5³. Here:

• 5 is the base (the rocket)
• 3 is the exponent (the number of boosters)

So, 5³ means 5 multiplied by itself 3 times:

5³ = 5 x 5 x 5 = 125

The bigger the exponent, the more the base is multiplied and the faster it zooms!

Here are some other examples:

• 2⁴ = 2 x 2 x 2 x 2 = 16
• 3² = 3 x 3 = 9
• 10¹ = 10 x 1 = 10 (anything to the power of 1 is just itself)

Exponents are used in all sorts of things, from science and engineering to finance and even music! They help us write big numbers in a compact way and make calculations much easier.

Here are some cool things you can do with exponents:

• Calculate the area of a square: If the side of a square is 5 meters, its area would be 5² square meters, which is 25 square meters.
• Figure out how much money you'll have in the future: If you save $100 every month for a year (12 months), you'll have 12 x $100 = $1200 at the end of the year.
• Compose music: Music notes can be written using fractions, and exponents can be used to shorten these fractions, making music easier to read and write.

So, the next time you see a number with a little booster rocket on top, remember, it's not just a number, it's a powerful tool that can help you explore the amazing world of math and beyond!

EXERCISE 1 - WRITING EXPONENTS

Here are 10 exercises on rewriting notations to exponents:

1. Rewrite 5 x 5 x 5 x 5 using exponents.
2. Express 7 multiplied by itself 4 times as an exponential expression.
3. Write 2 to the power of 4 as a repeated multiplication.
4. What is the exponent in the expression 10³?
5. What is the base in the expression 6²?
6. Rewrite 12 ÷ 12 ÷ 12 ÷ 12 using exponents.
7. Express 4⁵ as a product of repeated factors.
8. Write 3 x 3 x 3 x 3 x 3 in exponential notation.
9. What is the value of 2⁴?
10. What is the base in the expression 9 to the power of 3?

EXERCISE 2 - CALCULATING EXPONENTIAL VALUES

Exercise 2: Calculating Exponential Values

Put your exponent skills to the test with these 10 questions!

1. Evaluate 3².
2. Find the value of 5³.
3. Calculate 2⁴ + 4².
4. Solve for x in the equation 2^x = 16.
5. What is 7⁴ / 7²?
6. Simplify the expression (3 x 2)².
7. Calculate 10¹ + 10⁰. (Remember what happens with an exponent of 0!)
8. Find the missing exponent in the equation 4 x 4 = 4^□.
9. Express the year 2024 as a product of prime numbers using exponents.
10. Challenge yourself! Calculate 5^(3 + 2) - 5^2.

Bonus question: Can you explain the difference between 2³ and 3²?

Remember, have fun and use your calculator if needed!

Good luck!

EXERCISE 2 ANSWERS: 

Let's solve each mathematical expression:

1. \(3^2 = 9\)

2. \(5^3 = 125\)

3. \(2^4 + 4^2 = 16 + 16 = 32\)

4. \(2^x = 16 \Rightarrow x = 4\) (since \(2^4 = 16\))

5. \(7^4 / 7^2 = 2401 / 49 = 49\)

6. \((3 \times 2)^2 = 36\)

7. \(10^1 + 10^0 = 10 + 1 = 11\)

8. \(4 \times 4 = 4^2 \Rightarrow 16\)

9. Prime factorization of 2024: \(2^3 \times 3 \times 53\)

10. \(5^{3 + 2} - 5^2 = 5^5 - 5^2 = 3125 - 25 = 3100\)

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