Problem 531 Simplify each expression. $$\l... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 531

Simplify each expression. $$\left(a^{10}\right)^{y}$$

Short Answer

Expert verified

a^{10y}

Step by step solution

Understand the Power of a Power Rule

Recall that when you raise a power to another power, you multiply the exponents. This rule is written as $ (a^m)^n = a^{mn} $.

Identify the Exponents

In the given expression $ (a^{10})^y $, identify that $ m = 10 $ and $ n = y $.

Apply the Power of a Power Rule

Using the rule, multiply the exponents: $ a^{10 \times y} $.

Simplify the Expression

Write the expression with the new exponent: $ a^{10y} $.

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Key Concepts

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

Simplify Expressions

Simplifying expressions helps in making them easier to work with. In this problem, our goal is to take a complex expression, like $ \left(a^{10}\right)^{y} $, and transform it into a simpler form. Simplifying is essential for solving equations more easily and understanding mathematical relationships better. Break down the problem into steps, recognize patterns, and apply relevant rules like exponent rules. Taking it step-by-step ensures you understand each part of the expression and how to work with it.

Exponent Rules

Exponent rules are fundamental in algebra and are essential for working with expressions involving powers. The key rule here is the power of a power rule. This rule states that when you raise a power to another power, you multiply the exponents. Formally, it is written as $(a^m)^n = a^{mn}$. This rule simplifies the process of dealing with multiple layers of exponents in an expression.

The base stays the same 鈥� in our example, this is 'a'.
You multiply the exponents 鈥� here, the exponents are 10 and 'y' which become '10y'.

Understanding how and when to apply this rule is crucial for simplifying complex expressions effectively.

Multiplying Exponents

Multiplying exponents is one of the vital skills you need when simplifying expressions involving exponents. Remember, when multiplying exponents with the same base during a power of a power operation, you multiply the powers. For example, in $ \left(a^{10}\right)^{y} $:

First, recognize the base 'a'.
Next, identify the outer exponent 'y' and the inner exponent '10'.
Finally, multiply these exponents: $10 \times y = 10y $.

After performing these steps, you rewrite the expression as $a^{10y}$. This shows the new simplified form after applying the power of a power rule. Practicing these steps will help you handle more complex algebraic expressions with ease.

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91影视

Simplify each expression. $$\left(a^{10}\right)^{y}$$

Short Answer

Step by step solution

Understand the Power of a Power Rule

Identify the Exponents

Apply the Power of a Power Rule

Simplify the Expression

Key Concepts

Simplify Expressions

Exponent Rules

Multiplying Exponents

One App. One Place for Learning.

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