(a-2)^1/4 (a-2)^1/3

Suzhoumeite

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Jul 03, 2024

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Simplifying Expressions: (a-2)^1/4 and (a-2)^1/3

In this article, we will explore how to simplify two expressions: (a-2)^1/4 and (a-2)^1/3. These expressions involve rational exponents, which can be challenging to work with. However, by applying some basic properties of exponents, we can simplify these expressions and make them easier to understand.

(a-2)^1/4

To simplify (a-2)^1/4, we can start by rewriting the expression as:

(a-2)^(1/4) = ((a-2)^1)^(1/4)

Using the property of exponents that states (a^m)^n = a^(mn), we can rewrite the expression as:

((a-2)^1)^(1/4) = (a-2)^(1/4)

Now, we can simplify the expression by taking the fourth root of (a-2):

(a-2)^(1/4) = ∛(a-2)

So, the simplified form of (a-2)^1/4 is ∛(a-2).

(a-2)^1/3

To simplify (a-2)^1/3, we can follow a similar approach. We can start by rewriting the expression as:

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

Using the property of exponents that states (a^m)^n = a^(mn), we can rewrite the expression as:

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

Now, we can simplify the expression by taking the cube root of (a-2):

(a-2)^(1/3) = ∛(a-2)

So, the simplified form of (a-2)^1/3 is also ∛(a-2).

Conclusion

In conclusion, we have simplified two expressions: (a-2)^1/4 and (a-2)^1/3. By applying the property of exponents and taking the fourth root and cube root of (a-2), we have arrived at the simplified forms of ∛(a-2) for both expressions.