Rewrite the expression (dfrac{1}{y^{frac{5}{4}}}) in the form (y^{-n})….

Mathematics Questions

Rewrite the expression (dfrac{1}{y^{frac{5}{4}}}) in the form (y^{-n}).

Short Answer

To rewrite the expression, start by identifying the exponential terms, which are y^1 in the numerator and y^(5/4) in the denominator. After dividing the coefficients (both 1), subtract the exponents, leading to the final expression y^(-1/4).

Step-by-Step Solution

Step 1: Identify the Exponents

To begin rewriting the expression, start by identifying the exponential terms in both the numerator and the denominator. We have terms that look like y^1 in the numerator and y^(5/4) in the denominator. This is crucial as it allows us to easily apply the rules of exponents.

Step 2: Divide the Coefficients

Next, focus on the digit components of the expression. The digit term in our numerator is 1, and in the denominator, it is also 1. When dividing the coefficients, since 1 divided by 1 equals 1, this means our simplified expression will not require any additional changes to the coefficient.

Step 3: Subtract the Exponents

Finally, you’ll want to combine the terms by subtracting the exponent in the denominator from the exponent in the numerator. So, we will perform the operation: 1 – 5/4. This simplifies to -1/4. Therefore, the final expression can be rewritten as y^(-1/4), reflecting the rules of exponents.

Related Concepts

Exponential Terms

Terms in an expression that involve a base raised to a power, such as y^1 or y^(5/4)

Digit Components

Numeric values in an expression that can be divided or multiplied independently, such as the coefficients in the numerator and denominator

Subtract Exponents

The process of finding the difference between the exponents in an expression, typically used when dividing like bases, represented as the exponent of the numerator minus the exponent of the denominator.

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