Problem 24 Simplify. Show your steps. $$(... [FREE SOLUTION]

Chapter 1: Problem 24

Simplify. Show your steps. $$(5-3)(2+4)^{2}$$

Short Answer

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Question: Simplify the given algebraic expression: (5-3)(2+4)^2 Answer: 72

Step by step solution

Parentheses (Brackets)

First, handle the expressions inside parentheses. In our case, only the subtraction and addition are inside parentheses. $$(5-3)(2+4)^{2} = (2)(6)^{2}$$

Exponents

Next, handle any exponents. In this example, raise the simplified expression inside parentheses (6) to the power of 2: $$(2)(6)^{2} = (2)(36)$$

Multiplication

Finally, handle the multiplication operation: $$(2)(36) = 72$$ Thus, the simplified expression is $$72$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponents

Exponents might seem tricky at first, but they are simply a way of expressing repeated multiplication. Instead of writing something like $6 \times 6$, we can use an exponent and write it as $6^2$. The number above, in this case 2, is the exponent and tells us how many times the base (6) is multiplied by itself.

Exponents appear after the number they affect, like $x^n$, where $x$ is the base, and $n$ is the exponent.
It's crucial to handle exponents before any multiplication or division unless they're inside parentheses themselves.
Remember, any number to the power of zero is 1: $x^0 = 1$.

In the given problem, once the expression inside the parentheses is simplified, you raise $6$ to the power of 2, which gives $6 \times 6 = 36$. Understanding how to handle exponents will help simplify expressions quickly and accurately.

Parentheses

When you see parentheses in a math expression, they act like a highlighter, indicating which operations you should tackle first. Solving what's inside parentheses ensures that the foundational calculations are correct before moving on to exponents or multiplication operations.

Parentheses group numbers and operations together, establishing a clear order to follow.
Always simplify the expressions inside the parentheses before moving onto other operations.
Nesting may occur, with parentheses inside of other parentheses, which requires solving the innermost first.

For example, in the exercise $(5-3)(2+4)^2$, before thinking about those exponents or multiplication, you simplify to $(2)(6)^2$ by first calculating the expressions inside the parentheses. Solving within the parentheses first sets the stage for simplifying the overall expression effectively.

Simplifying Expressions

Simplifying expressions is a key skill in algebra, ultimately making the equations cleaner and easier to work with. The goal is to reduce complex expressions to simpler, more manageable forms without changing their value.

Start with parentheses, then move to exponents, and follow up with multiplication or division.
Perform each calculation step-by-step to avoid mistakes and to ensure clarity.
Keep an eye out for like terms and combine them whenever possible.

In simplifying the expression $(5-3)(2+4)^2$, each step is crucial for reducing the problem to a single number: 72. Progressing through the order of operations鈥攈andling parentheses, then exponents, followed by multiplication鈥攍eads to an efficient and accurate solution. Practicing this methodical approach will enhance your ability to handle more challenging expressions in the future.

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91影视

Simplify. Show your steps. $$(5-3)(2+4)^{2}$$

Short Answer

Step by step solution

Parentheses (Brackets)

Exponents

Multiplication

Key Concepts

Exponents

Parentheses

Simplifying Expressions

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