What is a different way to express a fractional exponent?

What is a different way to express a fractional exponent?

• A. Square root
• B. Cube root
• C. Exponential growth
• D. Polynomial

Answer: (A)

A fractional exponent can be expressed as a root. The numerator of the fractional exponent indicates the power to which the base is raised, while the denominator indicates the root taken. For example, a fractional exponent of 1/2 signifies that you are taking the square root of the base. Similarly, a fractional exponent of 1/3 would represent the cube root. This understanding stems from the rules of exponents, which state that \( a^{m/n} = \sqrt[n]{a^m} \), where \( m \) is the numerator and \( n \) is the denominator. Therefore, identifying a square root as an expression of a fractional exponent is accurate and demonstrates a principle of exponent manipulation in mathematics.

A fractional exponent can be expressed as a root. The numerator of the fractional exponent indicates the power to which the base is raised, while the denominator indicates the root taken. For example, a fractional exponent of 1/2 signifies that you are taking the square root of the base. Similarly, a fractional exponent of 1/3 would represent the cube root. This understanding stems from the rules of exponents, which state that ( a^{m/n} = \sqrt[n]{a^m} ), where ( m ) is the numerator and ( n ) is the denominator. Therefore, identifying a square root as an expression of a fractional exponent is accurate and demonstrates a principle of exponent manipulation in mathematics.