Basic Math Examples

Simplify ( fourth root of a^3y^2)/( fourth root of ay^3)
Step 1
Combine and into a single radical.
Step 2
Reduce the expression by cancelling the common factors.
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Step 2.1
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Cancel the common factor.
Step 2.4
Rewrite the expression.
Step 3
Cancel the common factor of and .
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Step 3.1
Factor out of .
Step 3.2
Cancel the common factors.
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factor.
Step 3.2.3
Rewrite the expression.
Step 4
Rewrite as .
Step 5
Simplify the numerator.
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Step 5.1
Rewrite as .
Step 5.2
Pull terms out from under the radical, assuming positive real numbers.
Step 6
Multiply by .
Step 7
Combine and simplify the denominator.
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Step 7.1
Multiply by .
Step 7.2
Raise to the power of .
Step 7.3
Use the power rule to combine exponents.
Step 7.4
Add and .
Step 7.5
Rewrite as .
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Step 7.5.1
Use to rewrite as .
Step 7.5.2
Apply the power rule and multiply exponents, .
Step 7.5.3
Combine and .
Step 7.5.4
Cancel the common factor of .
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Step 7.5.4.1
Cancel the common factor.
Step 7.5.4.2
Rewrite the expression.
Step 7.5.5
Simplify.
Step 8
Rewrite as .
Step 9
Simplify the numerator.
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Step 9.1
Rewrite the expression using the least common index of .
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Step 9.1.1
Use to rewrite as .
Step 9.1.2
Rewrite as .
Step 9.1.3
Rewrite as .
Step 9.2
Combine using the product rule for radicals.