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. For example, x^(1/2) is the square root of x.

Tags

CCSS.HSN.RN.A.2

Front

Convert the expression x^(3/4) into radical form.

Back

x^(3/4) = 4√(x^3) or (4√x)^3.

Tags

CCSS.HSN.RN.A.2

Front

What is the relationship between rational exponents and roots?

Back

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

Tags

CCSS.HSN.RN.A.2

Front

Simplify the expression (x^(1/2))^4.

Back

Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^2.

Tags

CCSS.8.EE.A.1

Front

What is the value of 8^(2/3)?

Back

8^(2/3) = (3√8)^2 = 4.

Front

How do you multiply expressions with rational exponents?

Back

To multiply expressions with rational exponents, add the exponents. For example, x^(1/2) * x^(1/3) = x^(1/2 + 1/3) = x^(5/6).

Tags

CCSS.HSN.RN.A.2

Front

What is the value of (27^(1/3))^2?

Back

(27^(1/3))^2 = 3^2 = 9.

Front

How do you divide expressions with rational exponents?

Back

To divide expressions with rational exponents, subtract the exponents. For example, x^(3/4) / x^(1/4) = x^(3/4 - 1/4) = x^(2/4) = x^(1/2).

Tags

CCSS.HSN.RN.A.2

Front

What is the simplified form of x^(5/2) * x^(3/2)?

Back

x^(5/2) * x^(3/2) = x^(5/2 + 3/2) = x^(8/2) = x^4.

Tags

CCSS.8.EE.A.1

Front

Convert the expression 16^(3/4) into radical form.

Back

16^(3/4) = 4√(16^3) = 4√(4096) = 16.

Tags

CCSS.HSN.RN.A.2