Trigonometry Examples

Rationalize the Denominator ( fourth root of b^9c^3)/( square root of bc)
Step 1
Simplify the numerator.
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Step 1.1
Rewrite as .
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Step 1.1.1
Factor out .
Step 1.1.2
Rewrite as .
Step 1.1.3
Add parentheses.
Step 1.2
Pull terms out from under the radical.
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
Raise to the power of .
Step 3.1.4
Use the power rule to combine exponents.
Step 3.1.5
Add and .
Step 3.1.6
Rewrite as .
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Step 3.1.6.1
Use to rewrite as .
Step 3.1.6.2
Apply the power rule and multiply exponents, .
Step 3.1.6.3
Combine and .
Step 3.1.6.4
Cancel the common factor of .
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Step 3.1.6.4.1
Cancel the common factor.
Step 3.1.6.4.2
Rewrite the expression.
Step 3.1.6.5
Simplify.
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 the expression using the least common index of .
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Step 4.1.1
Use to rewrite as .
Step 4.1.2
Rewrite as .
Step 4.1.3
Rewrite as .
Step 4.2
Combine using the product rule for radicals.
Step 4.3
Apply the product rule to .
Step 4.4
Combine exponents.
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Step 4.4.1
Raise to the power of .
Step 4.4.2
Use the power rule to combine exponents.
Step 4.4.3
Add and .
Step 4.4.4
Multiply by by adding the exponents.
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Step 4.4.4.1
Move .
Step 4.4.4.2
Use the power rule to combine exponents.
Step 4.4.4.3
Add and .
Step 5
Simplify the numerator.
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Step 5.1
Rewrite as .
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Step 5.1.1
Factor out .
Step 5.1.2
Reorder and .
Step 5.1.3
Add parentheses.
Step 5.2
Pull terms out from under the radical.
Step 6
Cancel the common factor of .
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Step 6.1
Cancel the common factor.
Step 6.2
Divide by .