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## Pre-algebra

### Course: Pre-algebra>Unit 6

Lesson 2: Substitution & evaluating expressions

# Evaluating exponent expressions with variables

In this math lesson, we learn to evaluate expressions with exponents and variables. We practice substituting values for variables and calculating the results. By mastering this skill, we can solve problems involving exponential expressions, enhancing our understanding of algebra and mathematical concepts.

## Want to join the conversation?

• What is (x+4)^2 = 25x^2? There need to be 2 answers.
• First, work out the expression to a form of ax^2 + bx + c = 0
``25x^2 – (x^2 + 8x + 16) = 025x^2 – x^2 – 8x – 16 = 024x^2 – 8x – 16 = 0``

Now, since 0 / n = 0, we can divide both sides by the shared factor of 8 among the terms

3x^2 – x – 2 = 0

The fact that a is not equal to 1 makes manual solving a little harder, but trying a few integer combinations gives us:
``(3x + 2)(x – 1) = 3x^2 – 3x + 2x – 2= 3x^2 – x – 23x + 2 = 0 or x – 1 = 03x = -2 or x = 1``

x = -2/3 or x = 1
• It still doesn't make sense to me because how does four twos make 16? Doesn't it equal 8?
• Four two's does equal 8. But 2 times 2 times 2 times 2 is equal to 16.
• At , wouldn't the -3^3 actually be -3*-3?
If the problem had parenthesis around the 3^2 then it would be 3*3.
• At , wouldn't the -3^3 actually be 2*3?
• It is 5^2-3^2, and exponents are repeated multiplication of the base, since base is 3, you multiply the base (3) the number of times of the expnnent (2). Thus, -3^2=-(3*3)=-9.
• 5-3=2, ^2+^2=^4, 2^4=16 but does it always work?
• You can't carry over a base and use the exponentiation symbol multiple times. Think of it like eating a banana. Your banana is gone after the operation; you'll need to get another one for the next operation, even if it's the same operation and the same banana.

Correct syntax would be:
``5 - 3 = 2.2^2 + 2^2 = 2*(2^2) = 2^1 * 2^2= 2^(2 + 1)``

[This is called the "product rule" of exponentation; b^p * b^q = b^(p + q)]

This is equal to 8, not 16! Also, the answer would've been no if it were true; you'd need to repeat the addition process the same amount of times as your exponent base for this to work!
• If you have a fraction
such as 8^2/2^4
can you first do the exponents and then find the value?
• Yep, that's quite right! However, to use the division rule of exponents, you must use the same base. We can take the greatest common divisor of the different bases and make this our new base!

2^(3*2) / 2^4 = 2^(6 - 4) = 2^2 = 4
• I'm so proud of myself for being able to solve these independently. When he tells us to pause the video, I can actually solve it with no explanation!
• can you teach step by step SLOWLY?