Converting and Evaluating Rational Exponents Practice

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) is the square root of x.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent to radical form, use the formula: a^(m/n) = n√(a^m), where m is the numerator and n is the denominator.

Front

Simplify: 2^(3/2)

Back

2^(3/2) = √(2^3) = √8 = 2√2.

Front

Simplify: 16^(1/4)

Back

16^(1/4) = 4, since 4^4 = 16.

Front

What is the value of 27^(2/3)?

Back

27^(2/3) = (3^3)^(2/3) = 3^2 = 9.

Front

Convert 81^(1/4) to radical form.

Back

81^(1/4) = 4√81 = 4*3 = 12.

Front

Simplify: (x^(1/2))^4

Back

(x^(1/2))^4 = x^(1/2 * 4) = x^2.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, a^(1/n) represents the n-th root of a.

Front

Simplify: 64^(3/2)

Back

64^(3/2) = (8^2)^(3/2) = 8^3 = 512.

Front

Convert 1/16 to a rational exponent.

Back

1/16 can be expressed as 16^(-1) or 16^(-2/2).