Basic Math Examples

Simplify ( square root of 75a^7b^4)/( square root of 40a^13c^9)
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
Cancel the common factor of and .
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Step 2.1.1
Factor out of .
Step 2.1.2
Cancel the common factors.
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Step 2.1.2.1
Factor out of .
Step 2.1.2.2
Cancel the common factor.
Step 2.1.2.3
Rewrite the expression.
Step 2.2
Cancel the common factor of and .
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Step 2.2.1
Factor out of .
Step 2.2.2
Cancel the common factors.
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Step 2.2.2.1
Factor out of .
Step 2.2.2.2
Cancel the common factor.
Step 2.2.2.3
Rewrite the expression.
Step 3
Simplify the numerator.
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Step 3.1
Rewrite as .
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Step 3.1.1
Factor the perfect power out of .
Step 3.1.2
Factor the perfect power out of .
Step 3.1.3
Rearrange the fraction .
Step 3.2
Pull terms out from under the radical.
Step 3.3
Rewrite as .
Step 3.4
Combine.
Step 3.5
Multiply by .
Step 3.6
Multiply by .
Step 3.7
Combine and simplify the denominator.
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Step 3.7.1
Multiply by .
Step 3.7.2
Move .
Step 3.7.3
Raise to the power of .
Step 3.7.4
Raise to the power of .
Step 3.7.5
Use the power rule to combine exponents.
Step 3.7.6
Add and .
Step 3.7.7
Rewrite as .
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Step 3.7.7.1
Use to rewrite as .
Step 3.7.7.2
Apply the power rule and multiply exponents, .
Step 3.7.7.3
Combine and .
Step 3.7.7.4
Cancel the common factor of .
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Step 3.7.7.4.1
Cancel the common factor.
Step 3.7.7.4.2
Rewrite the expression.
Step 3.7.7.5
Evaluate the exponent.
Step 3.8
Simplify the numerator.
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Step 3.8.1
Combine using the product rule for radicals.
Step 3.8.2
Multiply by .
Step 3.9
Multiply by .
Step 4
Combine and .
Step 5
Multiply the numerator by the reciprocal of the denominator.
Step 6
Combine.
Step 7
Multiply by .