Rational Exponents: Evaluating

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/n) is the nth root of x.

Front

How do you simplify an expression with a rational exponent?

Back

To simplify an expression with a rational exponent, rewrite it using radical notation. For example, a^(m/n) can be expressed as the nth root of a raised to the m power: (n√a)^m.

Front

What is the value of 27^(1/3)?

Back

The value of 27^(1/3) is 3, because 3^3 = 27.

Front

What is the value of 36^(1/2)?

Back

The value of 36^(1/2) is 6, because 6^2 = 36.

Front

What is the value of 8^(1/3)?

Back

The value of 8^(1/3) is 2, because 2^3 = 8.

Front

What is the value of 64^(1/2)?

Back

The value of 64^(1/2) is 8, because 8^2 = 64.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents provide a way to express roots. For example, a^(1/n) represents the nth root of a.

Front

How can you convert a radical expression to a rational exponent?

Back

To convert a radical expression to a rational exponent, express the root as a fraction. For example, √a can be written as a^(1/2).

Front

What is the simplified form of (x^(1/2))^2?

Back

The simplified form of (x^(1/2))^2 is x, because (1/2) * 2 = 1.

Front

What is the simplified form of (a^(1/3))^3?

Back

The simplified form of (a^(1/3))^3 is a, because (1/3) * 3 = 1.