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 simplify expressions with the same base and rational exponents?

Back

When simplifying expressions with the same base, you can add the exponents together if multiplying, or subtract them if dividing.

Front

What is the relationship between rational exponents and roots?

Back

A rational exponent can be expressed as a root; for example, x^(1/n) is equivalent to the n-th root of x.

Front

Simplify: 4^(1/3) x 4^(4/3)

Back

4^(5/3) because you add the exponents (1/3 + 4/3 = 5/3).

Front

What is the result of (x^(2/3))^4?

Back

x^(8/3) because you multiply the exponents (2/3 * 4 = 8/3).

Front

How do you express (5 x 3)^(2/3) in simplified form?

Back

15^(2/3) because you first multiply 5 and 3 to get 15, then apply the exponent.

Front

What does (3x)^(1/2) simplify to?

Back

√(3x) because the exponent 1/2 indicates the square root.

Front

What is the power of a product rule?

Back

The power of a product rule states that (ab)^n = a^n * b^n.

Front

What is the power of a quotient rule?

Back

The power of a quotient rule states that (a/b)^n = a^n / b^n.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent a^(m/n), write it as the n-th root of a raised to the m power: (n√a)^m.