Algebra Examples

Simplify ( cube root of x^3)/( fifth root of x^2)
Step 1
Pull terms out from under the radical, assuming real numbers.
Step 2
Multiply by .
Step 3
Simplify terms.
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Step 3.1
Combine and simplify the denominator.
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Step 3.1.1
Multiply by .
Step 3.1.2
Raise to the power of .
Step 3.1.3
Use the power rule to combine exponents.
Step 3.1.4
Add and .
Step 3.1.5
Rewrite as .
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Step 3.1.5.1
Use to rewrite as .
Step 3.1.5.2
Apply the power rule and multiply exponents, .
Step 3.1.5.3
Combine and .
Step 3.1.5.4
Multiply by .
Step 3.1.5.5
Cancel the common factor of and .
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Step 3.1.5.5.1
Factor out of .
Step 3.1.5.5.2
Cancel the common factors.
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Step 3.1.5.5.2.1
Factor out of .
Step 3.1.5.5.2.2
Cancel the common factor.
Step 3.1.5.5.2.3
Rewrite the expression.
Step 3.1.5.5.2.4
Divide by .
Step 3.2
Cancel the common factor of and .
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factors.
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Step 3.2.2.1
Factor out of .
Step 3.2.2.2
Cancel the common factor.
Step 3.2.2.3
Rewrite the expression.
Step 4
Simplify the numerator.
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Step 4.1
Rewrite as .
Step 4.2
Multiply the exponents in .
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Step 4.2.1
Apply the power rule and multiply exponents, .
Step 4.2.2
Multiply by .
Step 4.3
Factor out .
Step 4.4
Pull terms out from under the radical.
Step 5
Cancel the common factor of .
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Step 5.1
Cancel the common factor.
Step 5.2
Divide by .