Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is expressed as 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, it can be expressed as the n-th root of a raised to the m power: a^(m/n) = n√(a^m).

Front

What is the value of 2^(5/3)?

Back

2^(5/3) can be expressed as the cube root of 2^5, which is approximately 3.174.

Front

What does the negative exponent signify?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: a^(-n) = 1/(a^n).

Front

How do you simplify (5x)^(-1/2)?

Back

(5x)^(-1/2) can be simplified to 1/√(5x).

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 n-th root of a.

Front

How do you multiply expressions with the same base and rational exponents?

Back

When multiplying expressions with the same base, you add the exponents: a^(m/n) * a^(p/q) = a^((mq + np)/(nq)).

Front

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

Back

4^(4/3) can be expressed as the cube root of 4^4, which equals 4.

Front

How do you divide expressions with the same base and rational exponents?

Back

When dividing expressions with the same base, you subtract the exponents: a^(m/n) / a^(p/q) = a^((mq - np)/(nq)).

Front

What is (6v)^(3/2) in radical form?

Back

(6v)^(3/2) can be expressed as √((6v)^3) or (6v)^(3/2) = √(216v^3).