Simplify Fractional Exponents

Front

What is a fractional exponent?

Back

A fractional exponent represents both a power and a root. For example, x^(1/n) means the nth root of x.

Tags

CCSS.HSN.RN.A.2

Front

How do you simplify x^(m/n)?

Back

To simplify x^(m/n), rewrite it as the nth root of x raised to the m power: x^(m/n) = (n√x)^m.

Tags

CCSS.HSN.RN.A.2

Front

What is the relationship between fractional exponents and radicals?

Back

Fractional exponents can be expressed as radicals. For example, x^(1/2) is equivalent to √x.

Tags

CCSS.HSN.RN.A.2

Front

Simplify: x^(3/2)

Back

x^(3/2) = (√x)^3 = √(x^3).

Front

What does x^(0) equal?

Back

x^(0) = 1 for any non-zero x.

Tags

CCSS.8.EE.A.1

Front

What is the product rule for exponents?

Back

When multiplying like bases, add the exponents: x^a * x^b = x^(a+b).

Tags

CCSS.8.EE.A.1

Front

What is the quotient rule for exponents?

Back

When dividing like bases, subtract the exponents: x^a / x^b = x^(a-b).

Tags

CCSS.8.EE.A.1

Front

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

Back

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

Tags

CCSS.8.EE.A.1

Front

What is the power of a product rule?

Back

When raising a product to a power, distribute the exponent: (xy)^n = x^n * y^n.

Tags

CCSS.8.EE.A.1

Front

Simplify: (2x^(1/3))^3

Back

(2x^(1/3))^3 = 2^3 * (x^(1/3))^3 = 8x.