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^(m/n) to radical form, write it as (n-th root of a)^m.

Front

What is the value of 12^{3/4} in radical form?

Back

12^{3/4} = (√[4]{12})^3.

Front

What is the value of (-2)^3?

Back

The value of (-2)^3 is -8.

Front

What is the simplified form of 4^3?

Back

The simplified form of 4^3 is 64.

Front

What is the simplified form of 2^5?

Back

The simplified form of 2^5 is 32.

Front

What is 7^1?

Back

7^1 is equal to 7.

Front

How do you simplify an expression with a rational exponent?

Back

To simplify an expression with a rational exponent, convert it to radical form or apply the laws of exponents.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent both powers and roots; the denominator of the exponent indicates the root.

Front

What is the value of 8^{2/3}?

Back

8^{2/3} = (√[3]{8})^2 = 4.