Jika A Tidak Sama Dengan 0 Maka (-2a)^3(2a)^-2/3

5 min read Jun 26, 2024
Jika A Tidak Sama Dengan 0 Maka (-2a)^3(2a)^-2/3

Simplifying Algebraic Expressions: A Step-by-Step Guide

In this article, we will explore the simplification of the algebraic expression (-2a)^3(2a)^-2/3 under the condition a ≠ 0. We will follow a step-by-step approach to break down the expression and simplify it to its most basic form.

Step 1: Understand the Expression

The given expression is (-2a)^3(2a)^-2/3. This expression involves two terms: (-2a)^3 and (2a)^-2/3. Our goal is to simplify this expression by combining these two terms.

Step 2: Simplify the First Term

Let's start by simplifying the first term (-2a)^3. Using the power rule of exponents, which states that (ab)^n = a^n b^n, we can rewrite the term as:

(-2a)^3 = (-2)^3 a^3

Now, we can simplify the term by evaluating the cube of -2:

(-2)^3 = -8

So, the simplified first term is (-2a)^3 = -8a^3.

Step 3: Simplify the Second Term

Next, let's simplify the second term (2a)^-2/3. To simplify this term, we need to recall the rules of exponentiation. Specifically, we need to use the rule that states a^(-n) = 1/a^n.

Using this rule, we can rewrite the term as:

(2a)^-2/3 = 1/(2a)^(2/3)

Now, we can simplify the term further by evaluating the expression inside the parentheses:

1/(2a)^(2/3) = 1/(2^(2/3) a^(2/3))

Step 4: Combine the Terms

Now that we have simplified both terms, we can combine them to get the final expression. Recall that the original expression is a product of the two terms:

(-2a)^3(2a)^-2/3

Substituting the simplified terms, we get:

-8a^3(1/(2^(2/3) a^(2/3)))

Step 5: Simplify the Final Expression

To simplify the final expression, we can combine the terms by canceling out any common factors. Notice that a^3 and a^(2/3) have a common factor of a^(2/3). We can cancel out this term to get:

-8a^(3 - 2/3)/(2^(2/3))

Now, we can simplify the expression further by evaluating the exponents:

-8a^(7/3)/(2^(2/3))

Finally, we can simplify the expression to its most basic form:

-64a^(7/3)/4

Simplifying further, we get:

-16a^(7/3)

And that's the final answer!

Conclusion

In this article, we simplified the algebraic expression (-2a)^3(2a)^-2/3 under the condition a ≠ 0. By following a step-by-step approach, we broke down the expression into its component parts, simplified each term, and combined them to get the final answer. The simplified expression is -16a^(7/3).

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