The quotient property of radicals requires…

Mathematics Questions

The quotient property of radicals requires the indices to be the same. Does this mean that m b ‚Äã n a ‚Äã ‚Äã cannot be expressed as a single radical? Please explain.

Short Answer

The process involves identifying the base in the radicands to utilize rational exponents, simplifying the quotient by finding a common denominator and subtracting exponents, and finally expressing the result as the 4th root of y.

Step-by-Step Solution

Step 1: Identify the Base

First, recognize that the given radicands are powers with the same base. This is crucial because it allows us to express these powers using rational exponents, which makes it easier to manipulate the expressions mathematically.

Step 2: Simplify the Quotient

Next, simplify the quotient of the exponential expressions. To do this, follow these sub-steps:

  • Get a common denominator for the expressions.
  • Subtract the exponents based on the properties of exponents.
  • Apply the rules of exponents to simplify further.

Step 3: Express the Result

Finally, once the expression is simplified, determine its final form. The result should be expressed as the 4th root of y, indicating that you have achieved the required simplification and properly handled the exponents throughout the process.

Related Concepts

Base

The underlying number that is raised to a power in exponential expressions, crucial for simplifying powers with the same base.

Rational exponents

Exponents that are expressed as fractions, making it easier to manipulate and simplify expressions mathematically.

Properties of exponents

Fundamental rules that govern the operations of exponents, such as multiplying and dividing exponential terms, which allow for simplification and manipulation of expressions.

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