Convert the expressions to power form. (2)/(3(x^2+1)^-3)-(3 √((x^2+1)^7))/(4)

Name: Problem 84, Chapter 0: Finite Mathematics and Applied Calculus
Uploaded: 2021-08-28T16:51:15-08:00
Duration: 1 min 51 s
Channel: Julie Silva
Description: Convert the expressions to power form. (2)/(3(x^2+1)^-3)-(3 √((x^2+1)^7))/(4)

step 1 This problem, we're being asked to convert the given expression into power form. Well, in order

Convert the expressions to power form. (2)/(3(x^2+1)^-3)-(3...

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Key Concepts

Negative Exponents

Negative exponents indicate reciprocals, meaning that a term raised to a negative exponent is equivalent to one divided by that term raised to the corresponding positive exponent. This concept is crucial when rewriting expressions, as it allows one to move factors from the denominator to the numerator or vice versa.

Rational Exponents

Rational exponents provide a way to express roots as fractional powers. The numerator represents the power, while the denominator represents the root. This equivalence is used to convert radical expressions into power form, thereby simplifying the manipulation of algebraic expressions.

Conversion of Radical Expressions

Rewriting radical expressions in power form involves using rational exponents. For example, a cube root can be expressed as an exponent of one-third. This process standardizes the expression format and makes it easier to apply rules of exponents.

Properties of Exponents

Understanding the fundamental properties of exponents, such as the product rule, quotient rule, and power rule, is essential for manipulating and simplifying algebraic expressions. These rules allow for the consistent operation on terms with exponents and are instrumental in converting and simplifying expressions into a unified power form.

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