Trigonometry Examples

Simplify ( square root of (a+x)^3 cube root of (a+x)^2)/( fourth root of a+x)
Step 1
Simplify the numerator.
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Step 1.1
Rewrite the expression using the least common index of .
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Step 1.1.1
Use to rewrite as .
Step 1.1.2
Rewrite as .
Step 1.1.3
Rewrite as .
Step 1.1.4
Use to rewrite as .
Step 1.1.5
Rewrite as .
Step 1.1.6
Rewrite as .
Step 1.2
Combine using the product rule for radicals.
Step 1.3
Multiply by by adding the exponents.
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Step 1.3.1
Use the power rule to combine exponents.
Step 1.3.2
Add and .
Step 2
Simplify the numerator.
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Step 2.1
Rewrite as .
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Step 2.1.1
Factor out .
Step 2.1.2
Rewrite as .
Step 2.2
Pull terms out from under the radical.
Step 2.3
Rewrite as .
Step 2.4
Expand using the FOIL Method.
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Step 2.4.1
Apply the distributive property.
Step 2.4.2
Apply the distributive property.
Step 2.4.3
Apply the distributive property.
Step 2.5
Simplify and combine like terms.
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Step 2.5.1
Simplify each term.
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Step 2.5.1.1
Multiply by .
Step 2.5.1.2
Multiply by .
Step 2.5.2
Add and .
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Step 2.5.2.1
Reorder and .
Step 2.5.2.2
Add and .
Step 2.6
Apply the distributive property.
Step 2.7
Factor out of .
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Step 2.7.1
Factor out of .
Step 2.7.2
Factor out of .
Step 2.7.3
Factor out of .
Step 2.7.4
Factor out of .
Step 2.7.5
Factor out of .
Step 2.8
Factor using the perfect square rule.
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Step 2.8.1
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.8.2
Rewrite the polynomial.
Step 2.8.3
Factor using the perfect square trinomial rule , where and .
Step 3
Multiply by .
Step 4
Combine and simplify the denominator.
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Step 4.1
Multiply by .
Step 4.2
Raise to the power of .
Step 4.3
Use the power rule to combine exponents.
Step 4.4
Add and .
Step 4.5
Rewrite as .
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Step 4.5.1
Use to rewrite as .
Step 4.5.2
Apply the power rule and multiply exponents, .
Step 4.5.3
Combine and .
Step 4.5.4
Cancel the common factor of .
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Step 4.5.4.1
Cancel the common factor.
Step 4.5.4.2
Rewrite the expression.
Step 4.5.5
Simplify.
Step 5
Cancel the common factor of and .
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Step 5.1
Factor out of .
Step 5.2
Cancel the common factors.
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Step 5.2.1
Multiply by .
Step 5.2.2
Cancel the common factor.
Step 5.2.3
Rewrite the expression.
Step 5.2.4
Divide by .
Step 6
Apply the distributive property.
Step 7
Rewrite as .
Step 8
Apply the distributive property.
Step 9
Multiply .
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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 9.1.4
Use to rewrite as .
Step 9.1.5
Rewrite as .
Step 9.1.6
Rewrite as .
Step 9.2
Combine using the product rule for radicals.
Step 9.3
Multiply by by adding the exponents.
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Step 9.3.1
Use the power rule to combine exponents.
Step 9.3.2
Add and .
Step 10
Multiply .
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Step 10.1
Rewrite the expression using the least common index of .
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Step 10.1.1
Use to rewrite as .
Step 10.1.2
Rewrite as .
Step 10.1.3
Rewrite as .
Step 10.1.4
Use to rewrite as .
Step 10.1.5
Rewrite as .
Step 10.1.6
Rewrite as .
Step 10.2
Combine using the product rule for radicals.
Step 10.3
Multiply by by adding the exponents.
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Step 10.3.1
Use the power rule to combine exponents.
Step 10.3.2
Add and .