Evaluating -8h - 2(5 + F³) + 7g² Given F=-4, G=5, H=3/4

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Hey everyone! Today, let's dive into a fun math problem that involves evaluating an algebraic expression. We're given an expression with three variables, f, g, and h, and we're also given specific values for each of these variables. Our mission, should we choose to accept it (and we do!), is to substitute these values into the expression and simplify it to find the final answer. So, grab your thinking caps, and let's get started!

The Challenge: Unraveling the Expression

The expression we're tackling today is: -8h - 2(5 + f³) + 7g².** Sounds a bit intimidating, right? But don't worry, we'll break it down step by step. We know that f = -4, g = 5, and h = 3/4. The key here is to carefully substitute these values into the expression, paying close attention to the order of operations (PEMDAS/BODMAS). Remember, parentheses (or brackets) first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (also from left to right). This order is crucial to getting the correct answer.

Step 1: Substitution is Key

The very first thing we need to do is replace the variables in our expression with their given values. This is like replacing placeholders with the actual players on a sports team. So, wherever we see an f, we'll put in -4; wherever we see a g, we'll put in 5; and wherever we see an h, we'll put in 3/4. After this substitution, our expression looks like this:

-8(3/4) - 2(5 + (-4)³) + 7(5)²

See? It looks a bit less scary already! We've just replaced the letters with numbers. Now, the real fun begins – simplifying this expression. Think of it as peeling away the layers of an onion; we'll start with the innermost layers and work our way outwards.

Step 2: Exponents – Powering Through

According to the order of operations, we need to deal with exponents next. We have two terms with exponents in our expression: (-4)³ and (5)². Let's calculate these separately.

  • (-4)³ means -4 multiplied by itself three times: -4 * -4 * -4 = -64. Remember, a negative number raised to an odd power is negative.
  • (5)² means 5 multiplied by itself: 5 * 5 = 25.

Now, let's substitute these values back into our expression. Our expression now transforms into:

-8(3/4) - 2(5 + (-64)) + 7(25)

We've successfully powered through the exponents! Next up, we tackle the parentheses.

Step 3: Parentheses – Taming the Inner Beasts

Parentheses act like little cages, telling us to perform the operations inside them before anything else. In our expression, we have one set of parentheses: (5 + (-64)). This means we need to add 5 and -64 together.

5 + (-64) = -59

Now we replace the parentheses with this result, and our expression becomes:

-8(3/4) - 2(-59) + 7(25)

We're making great progress! The expression is becoming simpler and simpler. Now, we move on to multiplication.

Step 4: Multiplication – Multiplying Our Efforts

We have three multiplication operations in our expression: -8(3/4), -2(-59), and 7(25). Let's handle these one by one.

  • -8(3/4) means -8 multiplied by 3/4. We can think of -8 as -8/1, so we have (-8/1) * (3/4). Multiplying the numerators gives us -24, and multiplying the denominators gives us 4. So, we have -24/4, which simplifies to -6.
  • -2(-59) means -2 multiplied by -59. A negative times a negative is a positive, so -2 * -59 = 118.
  • 7(25) means 7 multiplied by 25, which equals 175.

Substituting these results back into our expression, we get:

-6 + 118 + 175

Look at how much simpler our expression has become! We've conquered the exponents and the parentheses, and we've successfully navigated the multiplication. Now, all that's left is addition.

Step 5: Addition – Summing It All Up

Finally, we reach the last step: addition. We have -6 + 118 + 175. Let's add these numbers together from left to right.

  • -6 + 118 = 112
  • 112 + 175 = 287

So, the final value of our expression is 287! We've cracked the code and solved the puzzle.

The Grand Finale: The Answer Revealed

After all our hard work, we've arrived at the final answer. The value of the expression -8h - 2(5 + f³) + 7g² when f = -4, g = 5, and h = 3/4 is 287. Congratulations, mathletes! You've successfully navigated through parentheses, exponents, multiplication, and addition to arrive at the correct solution. Remember, the key to solving these types of problems is to break them down into smaller, manageable steps and to carefully follow the order of operations. Keep practicing, and you'll become a math whiz in no time!

To ensure clarity and searchability, let's fine-tune our keywords and the original question. It's crucial that both are as precise and easy to understand as possible. This helps others who might be searching for similar problems find our solution more effectively.

Refining the Keywords

Our primary keywords should directly reflect the problem's core concepts. In this case, we're dealing with evaluating an algebraic expression given specific variable values. Here's a refined set of keywords:

  • Evaluating algebraic expressions: This keyword captures the fundamental task at hand.
  • Substituting variables: This highlights the core technique used to solve the problem.
  • Order of operations (PEMDAS/BODMAS): This emphasizes the critical mathematical principle that governs the solution process.
  • Expression simplification: This describes the overall goal of reducing the expression to its simplest form.
  • f = -4, g = 5, h = 3/4: These specify the given variable values, making it easier for someone with the same values to find the solution.

These keywords are more targeted than generic terms like “math problem” or “algebra.” They directly address the specific concepts involved, improving searchability and relevance.

Sharpening the Question

The original question, while clear, can be made even more precise. We want to ensure there's no ambiguity and that the question immediately conveys the task.

Original Question: What is the value of the expression when f=-4, g=5, and h=3/4? -8h - 2(5 + f³) + 7g²

Revised Question: Evaluate the algebraic expression -8h - 2(5 + f³) + 7g² given that f = -4, g = 5, and h = 3/4.

The revised question is more direct and uses stronger action verbs like