Rational Exponents and Radicals

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^(m/n) means the n-th root of x raised to the m-th power.

Front

How do you convert a radical expression to an exponential expression?

Back

To convert a radical expression to an exponential expression, use the formula: √[n]{x} = x^(1/n). For example, ∛x = x^(1/3).

Front

Simplify: 2^(3/2)

Back

2^(3/2) = √(2^3) = √8 = 2√2.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots. For example, x^(1/n) is equivalent to the n-th root of x.

Front

Rewrite in radical form: x^(3/4)

Back

x^(3/4) = 4√(x^3).

Front

Simplify: 4^(1/2)

Back

4^(1/2) = √4 = 2.

Front

What is the value of 27^(2/3)?

Back

27^(2/3) = (3^3)^(2/3) = 3^(3*2/3) = 3^2 = 9.

Front

Write in exponential form: ∛(x^5)

Back

∛(x^5) = x^(5/3).

Front

Simplify: (x^(1/2))^4

Back

(x^(1/2))^4 = x^(1/2 * 4) = x^2.

Front

What is the value of 16^(3/4)?

Back

16^(3/4) = (2^4)^(3/4) = 2^(4*3/4) = 2^3 = 8.