Pre-Algebra Examples

Solve for x (x-5)^(2/3)=4
Step 1
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 2
Simplify the exponent.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Simplify .
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Step 2.1.1.1
Multiply the exponents in .
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Step 2.1.1.1.1
Apply the power rule and multiply exponents, .
Step 2.1.1.1.2
Cancel the common factor of .
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Step 2.1.1.1.2.1
Cancel the common factor.
Step 2.1.1.1.2.2
Rewrite the expression.
Step 2.1.1.1.3
Cancel the common factor of .
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Step 2.1.1.1.3.1
Cancel the common factor.
Step 2.1.1.1.3.2
Rewrite the expression.
Step 2.1.1.2
Simplify.
Step 2.2
Simplify the right side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Simplify the expression.
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Step 2.2.1.1.1
Rewrite as .
Step 2.2.1.1.2
Apply the power rule and multiply exponents, .
Step 2.2.1.2
Cancel the common factor of .
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Step 2.2.1.2.1
Cancel the common factor.
Step 2.2.1.2.2
Rewrite the expression.
Step 2.2.1.3
Raise to the power of .
Step 3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.1
First, use the positive value of the to find the first solution.
Step 3.2
Move all terms not containing to the right side of the equation.
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Step 3.2.1
Add to both sides of the equation.
Step 3.2.2
Add and .
Step 3.3
Next, use the negative value of the to find the second solution.
Step 3.4
Move all terms not containing to the right side of the equation.
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Step 3.4.1
Add to both sides of the equation.
Step 3.4.2
Add and .
Step 3.5
The complete solution is the result of both the positive and negative portions of the solution.