IXL - Solve equations with rational exponents (Precalculus practice)

Solve for

(

–

)

–

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

ref_doc_title.

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

(

–

)

(

–

)

–

(

–

)

Add 15 to both sides

Next, isolate

–

by raising both sides of the equation to the

power.

(

–

)

–

256

Finish solving for

Add 4 to both sides

260

Add 4 to both sides

Divide both sides by 10

There is one potential solution,

Check to see if it is extraneous.

(

–

)

–

(

–

)

–

≟

(

260

–

)

–

≟

256

–

≟

256

–

≟

–

≟

–

≟

satisfies the original equation, so it is not extraneous.

The equation has one solution,

Looking for more? Try these:

Lesson: Rational exponents

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

M.1Evaluate rational exponents

D.6Solve a quadratic equation by factoring

Lesson: Rational exponents

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!