Basic Math Examples

Simplify ((( square root of a)^3* fourth root of a^5)^2)÷( square root of a^7)
Step 1
Rewrite the division as a fraction.
Step 2
Simplify the numerator.
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Step 2.1
Apply the product rule to .
Step 2.2
Multiply the exponents in .
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Step 2.2.1
Apply the power rule and multiply exponents, .
Step 2.2.2
Multiply by .
Step 2.3
Rewrite as .
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Step 2.3.1
Use to rewrite as .
Step 2.3.2
Apply the power rule and multiply exponents, .
Step 2.3.3
Combine and .
Step 2.3.4
Cancel the common factor of and .
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Step 2.3.4.1
Factor out of .
Step 2.3.4.2
Cancel the common factors.
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Step 2.3.4.2.1
Factor out of .
Step 2.3.4.2.2
Cancel the common factor.
Step 2.3.4.2.3
Rewrite the expression.
Step 2.3.4.2.4
Divide by .
Step 2.4
Factor out .
Step 2.5
Pull terms out from under the radical.
Step 2.6
Apply the product rule to .
Step 2.7
Rewrite as .
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Step 2.7.1
Use to rewrite as .
Step 2.7.2
Apply the power rule and multiply exponents, .
Step 2.7.3
Combine and .
Step 2.7.4
Cancel the common factor of and .
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Step 2.7.4.1
Factor out of .
Step 2.7.4.2
Cancel the common factors.
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Step 2.7.4.2.1
Factor out of .
Step 2.7.4.2.2
Cancel the common factor.
Step 2.7.4.2.3
Rewrite the expression.
Step 2.7.5
Rewrite as .
Step 2.8
Multiply by by adding the exponents.
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Step 2.8.1
Use the power rule to combine exponents.
Step 2.8.2
Add and .
Step 3
Simplify the denominator.
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Step 3.1
Rewrite as .
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Step 3.1.1
Factor out .
Step 3.1.2
Rewrite as .
Step 3.2
Pull terms out from under the radical.
Step 4
Reduce the expression by cancelling the common factors.
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Step 4.1
Cancel the common factor of and .
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Step 4.1.1
Factor out of .
Step 4.1.2
Cancel the common factors.
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Step 4.1.2.1
Factor out of .
Step 4.1.2.2
Cancel the common factor.
Step 4.1.2.3
Rewrite the expression.
Step 4.2
Cancel the common factor of .
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Step 4.2.1
Cancel the common factor.
Step 4.2.2
Divide by .