Problem 86 - Algebra 1

Question

Evaluate the expression for the given value of the variable. $$5 y^{3} \text { when } y=4$$

Step-by-Step Solution

Answer

The value of the expression \(5y^3\) when \(y = 4\) is 320.

Step 1: Substitute

The first step is to substitute the value of \(y\) given, which is 4, into the expression \(5y^3\). This gives us \(5(4)^3\).

Step 2: Simplify

Next, we follow the order of operations. Start by calculating the cube of 4, which is \(4^3 = 4*4*4 = 64\). Then we multiply this by 5 to obtain \(5 * 64\).

Step 3: Calculate

Finally, by multiplying 5 and 64 together, the outcome will be 320. Therefore, the value of the expression \(5y^3\) when \(y = 4\) is 320.

Key Concepts

Substitution Made Easy

Substitution is like replacing friends in a game. When evaluating expressions, we plug in known values for variables. If your teacher gives you a mystery box with a letter, like `y`, and tells you what's inside, that's when substitution happens. It's simple! Just replace every `y` with the given number.

For our exercise, when we have the expression \(5y^3\) and \(y = 4\), we substitute 4 for each `y`. So, \(5y^3\) becomes \(5(4)^3\).

Think of it like swapping a toy in a box with the exact same toy. The appearance might change, but the value does not. It's a handy trick that sets the stage for all the exciting calculations to follow.

Mastering the Order of Operations

When solving any math problem, following the right steps is crucial. This way, you get the correct answer systematically. This list of rules is known as the order of operations, and it tells us the order in which to perform different math operations.

Remember the acronym PEMDAS which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In our exercise, once we've handled substitution, we compute the exponent first. That is \(4^3\). Afterward, we do the multiplication \(5 \times 64\).

Always follow these steps to ensure you never miss a beat in your calculations. It's like dancing to your favorite song, every step is important.

Understanding and Applying Exponents

Exponents are fantastic! They help us express repeated multiplication of the same number. In our case, we have \(4^3\). This means 4 is multiplied by itself three times: \(4 \times 4 \times 4\).

Now, to calculate \(4^3\):

• First, multiply the first two 4's together, giving us 16.
• Next, multiply this result by another 4, resulting in 64.

You see, exponents make life easier by telling us how many times to use a number in multiplication.

Once you've cracked the code on exponents, you'll see how powerful they are as a math tool. It's like having a trusty calculator in your mind, always ready to simplify your math expressions.