Solving Equations with 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.

Tags

CCSS.HSN.RN.A.2

Front

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

Back

To convert a radical expression to a rational exponent, express the root as a denominator and the power as a numerator. For example, √x = x^(1/2).

Tags

CCSS.HSN.RN.A.2

Front

What is the general form of the power rule for exponents?

Back

The power rule states that (a^m)^n = a^(m*n).

Tags

CCSS.8.EE.A.1

Front

How do you solve an equation with a rational exponent?

Back

To solve an equation with a rational exponent, isolate the term with the exponent and raise both sides to the reciprocal of the rational exponent.

Front

What is the reciprocal of a rational exponent?

Back

The reciprocal of a rational exponent a^(m/n) is a^(n/m).

Tags

CCSS.HSN.RN.A.2

Front

Solve for x: (x + 2)^(3/2) = 8

Back

x = 6.

Front

Rewrite the expression without using a radical: (x + 3)^(1/2)

Back

(x + 3)^(1/2) is already in rational exponent form.

Front

What is the first step in solving (2x - 1)^(3/4) + 9 = 36?

Back

Subtract 9 from both sides to isolate the term with the rational exponent.

Front

Solve for x: (3x - 4)^(1/3) = 2

Back

x = 10/3.

Front

What does it mean to simplify an expression with rational exponents?

Back

Simplifying an expression with rational exponents means rewriting it in a more manageable form, often eliminating radicals.