Trigonometry Examples

Rationalize the Denominator ( cube root of 5x)/( cube root of 4y^7)
Step 1
Simplify the denominator.
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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
Reorder and .
Step 1.1.4
Add parentheses.
Step 1.2
Pull terms out from under the radical.
Step 2
Multiply by .
Step 3
Combine and simplify the denominator.
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Step 3.1
Multiply by .
Step 3.2
Move .
Step 3.3
Raise to the power of .
Step 3.4
Use the power rule to combine exponents.
Step 3.5
Add and .
Step 3.6
Rewrite as .
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Step 3.6.1
Use to rewrite as .
Step 3.6.2
Apply the power rule and multiply exponents, .
Step 3.6.3
Combine and .
Step 3.6.4
Cancel the common factor of .
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Step 3.6.4.1
Cancel the common factor.
Step 3.6.4.2
Rewrite the expression.
Step 3.6.5
Simplify.
Step 4
Multiply by by adding the exponents.
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Step 4.1
Move .
Step 4.2
Multiply by .
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Step 4.2.1
Raise to the power of .
Step 4.2.2
Use the power rule to combine exponents.
Step 4.3
Add and .
Step 5
Simplify the numerator.
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Step 5.1
Rewrite as .
Step 5.2
Apply the product rule to .
Step 5.3
Raise to the power of .
Step 5.4
Rewrite as .
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Step 5.4.1
Factor out of .
Step 5.4.2
Rewrite as .
Step 5.4.3
Add parentheses.
Step 5.5
Pull terms out from under the radical.
Step 5.6
Combine exponents.
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Step 5.6.1
Combine using the product rule for radicals.
Step 5.6.2
Multiply by .
Step 6
Reduce the expression by cancelling the common factors.
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Step 6.1
Cancel the common factor of and .
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Step 6.1.1
Factor out of .
Step 6.1.2
Cancel the common factors.
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Step 6.1.2.1
Factor out of .
Step 6.1.2.2
Cancel the common factor.
Step 6.1.2.3
Rewrite the expression.
Step 6.2
Move to the left of .