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

How do you convert a rational exponent to a radical expression?

Back

To convert a rational exponent to a radical expression, use the formula a^(m/n) = n√(a^m), where m is the numerator and n is the denominator.

Tags

CCSS.HSN.RN.A.2

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, an exponent of 1/3 corresponds to the cube root.

Tags

CCSS.HSN.RN.A.2

Front

Simplify the expression: 16^(3/4).

Back

16^(3/4) = (16^(1/4))^3 = (2)^3 = 8.

Front

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

Back

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

Front

If x^(1/2) = 4, what is the value of x?

Back

x = 4^2 = 16.

Front

How do you multiply expressions with rational exponents?

Back

To multiply expressions with rational exponents, add the exponents if the bases are the same: a^(m/n) * a^(p/q) = a^((mq + np)/(nq)).

Tags

CCSS.8.EE.A.1

Front

What is the result of (x^(1/3))^6?

Back

The result is x^(6/3) = x^2.

Tags

CCSS.HSA.APR.A.1

Front

How do you divide expressions with rational exponents?

Back

To divide expressions with rational exponents, subtract the exponents if the bases are the same: a^(m/n) / a^(p/q) = a^((mq - np)/(nq)).

Tags

CCSS.8.EE.A.1

Front

What is the value of (64^(1/2))^4?

Back

(64^(1/2))^4 = (8)^4 = 4096.