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

Front

How do you solve an equation with a negative rational exponent?

Back

To solve an equation with a negative rational exponent, first rewrite the expression using a positive exponent. For example, x^(-3/4) = 1/(x^(3/4)). Then solve for x.

Front

What is the first step in solving x^(-3/4) = 8?

Back

Rewrite the equation as 1/(x^(3/4)) = 8, then multiply both sides by x^(3/4) to isolate x.

Front

If (x-2)^(1/3) = 5, what is the next step to solve for x?

Back

Cube both sides of the equation to eliminate the exponent: x - 2 = 5^3.

Front

What does it mean to cube a number?

Back

Cubing a number means raising it to the power of three, which is multiplying the number by itself three times.

Front

How do you isolate x in the equation 2x^(3/4) = 54?

Back

Divide both sides by 2 to get x^(3/4) = 27, then raise both sides to the power of 4/3 to solve for x.

Front

What is the solution to the equation x^(1/3) - 7 = 0?

Back

Add 7 to both sides to get x^(1/3) = 7, then cube both sides to find x = 343.

Front

What is the significance of the denominator in a rational exponent?

Back

The denominator indicates the root to be taken. For example, in x^(m/n), n is the root and m is the power.

Front

How do you solve the equation 2(x-3)^(2/3) - 10 = -2?

Back

First, add 10 to both sides to get 2(x-3)^(2/3) = 8, then divide by 2 to isolate (x-3)^(2/3) = 4.

Front

What is the process to eliminate a fractional exponent?

Back

Raise both sides of the equation to the reciprocal of the fractional exponent. For example, if you have x^(m/n), raise both sides to n/m.