Problem 51 Write each expression without us... [FREE SOLUTION]

91影视

Beginning Algebra: A Guided Approach

Rosemary Karr, Marilyn Massey, R. David Gustafson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 4: Problem 51

Write each expression without using exponents. $$-2 y^{4}$$

Short Answer

Expert verified

The expression $-2 y^{4}$ without using exponents can be written as $-2 * (y * y * y * y)$.

Step by step solution

Understand the concept of exponent

The exponent $4$ on $y$ in the given expression $-2 y^{4}$ means $y$ is multiplying itself four times. Thus, $y^4$ can be rewritten as $y*y*y*y$.

Rewrite the expression

We can now substitute $y^4$ with $y*y*y*y$ in the given expression, thus without using exponents, $-2 y^{4}$ can be written as $-2 * (y * y* y* y)$.

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Key Concepts

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

Exponents

Exponents are a fundamental part of algebra that help us simplify expressions. When you have something like $ y^4 $, the exponent $4$ is telling you that the base $y$ is multiplied by itself four times. This is a compact way to show repeated multiplication. Instead of writing $ y \cdot y \cdot y \cdot y $, we just write $ y^4 $.
Exponents follow certain rules that make them especially useful:

Rule of Multiplication (Product Rule): When multiplying like bases with exponents, you add the exponents. For instance, $ y^m \cdot y^n = y^{m+n} $.
Power of a Power Rule: When you raise an exponent to another power, you multiply the exponents. For example, $ (y^m)^n = y^{m\cdot n} $.
Zero Exponent Rule: Any non-zero base raised to the power of zero is 1, such as $ y^0 = 1 $.

Understanding these rules can greatly simplify complex expressions and make calculations easier.

Expressions

Expressions in algebra are combinations of numbers, variables, and operations. They do not have an equal sign鈥攖hat would make them equations. In the expression $-2 y^4$, there are several parts to consider:

Constant: The $-2$ is a constant term, which means it is a fixed number.
Variable: The $y$ is a variable, which means it can change values depending on what you're solving for.
Exponent: The $^4$ in $y^4$ is the exponent, as explained earlier.
Product: The entire expression $-2 y^4$ represents the product of $-2$ and $y^4$.

When simplifying expressions without exponents, break them down into their basic multiplication components to make it easier to manipulate and solve problems.

Multiplication

Multiplication is one of the basic operations in mathematics. It's essentially repeated addition. In expressions involving exponents, multiplication becomes crucial because you might have to multiply the same number several times, like in $y^4$ which means multiplying $y$ by itself four times.
When you're faced with expressions involving multiplication, here are a few things to remember:

Order Doesn't Matter: Multiplication is commutative, meaning $a\cdot b = b\cdot a$.
Multiplying by One: Any number multiplied by 1 remains unchanged, i.e., $ a\cdot 1 = a $.
Multiplying by Zero: Any number multiplied by 0 is 0, i.e., $ a\cdot 0 = 0 $.

Understanding these properties can help manage and solve expressions effectively. In the exercise, rewriting $-2 y^4$ as $-2 \cdot (y \cdot y \cdot y \cdot y)$ illustrates how multiplication ties together constants, variables, and exponents.

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91影视

Write each expression without using exponents. $$-2 y^{4}$$

Short Answer

Step by step solution

Understand the concept of exponent

Rewrite the expression

Key Concepts

Exponents

Expressions

Multiplication

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