Here are the essential concepts you must grasp in order to answer the question correctly.
Rationalizing the Denominator
Rationalizing the denominator involves eliminating any irrational numbers from the denominator of a fraction. This is typically achieved by multiplying both the numerator and the denominator by a suitable expression that will result in a rational number in the denominator. For example, if the denominator is a square root, multiplying by the same square root can help achieve this.
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Simplifying Radicals
Simplifying radicals refers to the process of reducing a square root or other root to its simplest form. This involves factoring out perfect squares or other factors from under the radical sign. For instance, √18 can be simplified to 3√2, as 18 = 9 × 2 and √9 = 3.
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Properties of Exponents
Properties of exponents are rules that govern how to manipulate expressions involving powers. Key properties include the product of powers, quotient of powers, and power of a power. Understanding these properties is essential when simplifying expressions that involve roots, as they help in rewriting and reducing terms effectively.
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