Which expression is equivalent to 8y10 8y50 32y10 32y50 – In the realm of algebra, equivalent expressions hold a pivotal role, providing alternative representations of the same mathematical concept. Among these expressions, those involving exponents demand a deeper understanding of the underlying rules. This article embarks on a journey to unravel the intricacies of simplifying exponents, culminating in the equivalence of 8y^10, 8y^50, 32y^10, and 32y^50.

Our exploration delves into the fundamental principles of exponent simplification, examining the processes of factoring and combining like terms. Through a step-by-step demonstration, we unveil the techniques for organizing and presenting equivalent expressions in a clear and concise manner.

Equivalent Expressions and Simplifying Exponents: Which Expression Is Equivalent To 8y10 8y50 32y10 32y50

In mathematics, equivalent expressions are those that have the same value regardless of the input. Understanding equivalent expressions is crucial for simplifying complex algebraic expressions and solving equations.

Simplifying Exponents

When multiplying terms with the same base, the exponents can be added. For example:

8y¹⁰– 8y ⁵⁰= 8 ²– y ¹⁰⁺⁵⁰= 64y ⁶⁰

Similarly, when dividing terms with the same base, the exponents can be subtracted.

Factoring and Combining Like Terms, Which expression is equivalent to 8y10 8y50 32y10 32y50

Factoring involves identifying and removing common factors from an expression. For instance, in the given expressions, 8y ¹⁰can be factored out:

8y¹⁰– 8y ⁵⁰= 8y ¹⁰– 8y ¹⁰– y ⁴⁰

Like terms are those with the same variable and exponent. In this case, 8y ¹⁰can be combined to simplify further:

8y¹⁰– 8y ¹⁰– y ⁴⁰= (8 – 8) – (y ¹⁰– y ¹⁰) – y ⁴⁰= 64y ²⁰– y ⁴⁰= 64y ⁶⁰

Organizing and Presenting Results

To organize the given expressions and their simplified forms, we can create an HTML table:

Key Questions Answered

What is the concept of equivalent expressions?

Equivalent expressions are mathematical expressions that represent the same value despite having different appearances.

How can I simplify exponents when multiplying terms with the same base?

To simplify exponents when multiplying terms with the same base, add the exponents of the like bases.