Question

What value of $r$ makes $y^{28}=y^{3 r} \cdot y^{7}$ true?

   What value of $r$ makes $y^{28}=y^{3 r} \cdot y^{7}$ true?

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 6, Problem 39

Instant Answer

Solved by Expert Ashley High

03/03/2020

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Step 1: We are given the equation $y^{28}=y^{3 r} \cdot y^{7}$. Show more…

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What value of $r$ makes $y^{28}=y^{3 r} \cdot y^{7}$ true?

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Key Concepts

Laws_of_Exponents

These rules govern how exponents behave under various operations such as multiplication, division, and taking powers of powers. They provide a systematic way to simplify and rewrite expressions involving exponential notation, ensuring consistency across algebraic manipulations.

Product_of_Powers Property

This property states that when multiplying two expressions with the same base, you can add their exponents together (i.e., a^m * a^n = a^(m+n)). It is essential for simplifying the product of exponential expressions and reducing more complex equations to a manageable form.

Equating Exponents in Exponential Equations

When two exponential expressions with the same nonzero base are equal, their exponents must necessarily be equal. This principle allows for solving equations by setting the exponents equal to each other, providing a straightforward method for determining unknown variables in the exponents.

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