Algebra Examples

Simplify ( square root of 6x^8y^9)/( square root of 5x^2y^4)
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
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Cancel the common factor.
Step 2.4
Rewrite the expression.
Step 3
Cancel the common factor of and .
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Step 3.1
Factor out of .
Step 3.2
Cancel the common factors.
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factor.
Step 3.2.3
Rewrite the expression.
Step 4
Rewrite as .
Step 5
Simplify the numerator.
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Step 5.1
Rewrite as .
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Step 5.1.1
Rewrite as .
Step 5.1.2
Factor out .
Step 5.1.3
Rewrite as .
Step 5.1.4
Move .
Step 5.1.5
Rewrite as .
Step 5.1.6
Add parentheses.
Step 5.2
Pull terms out from under the radical.
Step 6
Multiply by .
Step 7
Combine and simplify the denominator.
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Step 7.1
Multiply by .
Step 7.2
Raise to the power of .
Step 7.3
Raise to the power of .
Step 7.4
Use the power rule to combine exponents.
Step 7.5
Add and .
Step 7.6
Rewrite as .
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Step 7.6.1
Use to rewrite as .
Step 7.6.2
Apply the power rule and multiply exponents, .
Step 7.6.3
Combine and .
Step 7.6.4
Cancel the common factor of .
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Step 7.6.4.1
Cancel the common factor.
Step 7.6.4.2
Rewrite the expression.
Step 7.6.5
Evaluate the exponent.
Step 8
Simplify the numerator.
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Step 8.1
Combine using the product rule for radicals.
Step 8.2
Multiply by .