3.1 Precalculus Practice - Rational Exponents

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.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent a/b to radical form, write it as the b-th root of a raised to the power of a: x^(a/b) = b√(x^a).

Front

Simplify: 5^(3/2)

Back

125

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent both powers and roots, allowing expressions to be simplified using either method.

Front

Rewrite 27^(1/3) in radical form.

Back

3√27

Front

Simplify: (16^(1/2))^2

Back

16

Front

Convert the expression 1/4 to exponential form.

Back

4^(-1) or 4^(1/4) depending on context.

Front

What is the value of 64^(2/3)?

Back

16

Front

How do you simplify the expression (x^(1/2))^4?

Back

x^2

Front

What is the value of 81^(3/4)?

Back

27