IXL - Solve equations with rational exponents (Algebra 2 practice)

Solve for

(

–

)

–

Write one solution in each box. You can add or remove boxes. If there are no solutions, remove all boxes.

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Learn with an example

question

Solve for

(

–

)

Write one solution in each box. You can add or remove boxes. If there are no solutions, remove all boxes.

key idea

When solving an equation, it is sometimes necessary to raise both sides of the equation to the same power. However, this can introduce extraneous

solutions.

These are values that satisfy the equation after raising both sides to the same power, but do not satisfy the original equation. Here's why this happens:

it isn't always true that

For example,

(

–

)

but

≠

–

Consider the equation

Only one value satisfies this equation,

If you square both sides of the equation, you get

(

)

There are two values that satisfy this new equation,

and

–

But only

made the original equation true, so

–

is extraneous.

Tip:

When you raise both sides of an equation to the same power, you should check to see if any of your solutions are extraneous. A potential solution is extraneous if evaluating the original equation with it results in a false statement.

solution

To solve for

first isolate

(

–

)

(

–

)

(

–

)

Subtract 15 from both sides

Next, isolate

–

by raising both sides of the equation to the 5th power.

(

–

)

–

243

Finish solving for

Divide both sides by

–

Divide both sides by

–

There is one potential solution,

–

Check to see if it is extraneous.

(

–

)

(

–

(

–

)

≟

243

≟

243

≟

–

satisfies the original equation, so it is not extraneous.

The equation has one solution,

–

Looking for more? Try these:

Lesson: Rational exponents

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Teacher tools

Work it out

Not feeling ready yet? These can help:

T.1Evaluate rational exponents

O.3Solve a quadratic equation by factoring

Lesson: Rational exponents

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