Precalculus Examples

Simplify ((x^-3y^2)^-4)/((y^6x^-4)^-2)
Step 1
Simplify the expression.
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Step 1.1
Move to the denominator using the negative exponent rule .
Step 1.2
Move to the numerator using the negative exponent rule .
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
Multiply the exponents in .
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Step 2.3.1
Apply the power rule and multiply exponents, .
Step 2.3.2
Multiply by .
Step 2.4
Rewrite the expression using the negative exponent rule .
Step 3
Simplify the denominator.
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Step 3.1
Apply the product rule to .
Step 3.2
Multiply the exponents in .
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Step 3.2.1
Apply the power rule and multiply exponents, .
Step 3.2.2
Multiply by .
Step 3.3
Rewrite the expression using the negative exponent rule .
Step 3.4
Multiply the exponents in .
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Step 3.4.1
Apply the power rule and multiply exponents, .
Step 3.4.2
Multiply by .
Step 4
Combine fractions.
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Step 4.1
Combine and .
Step 4.2
Combine and .
Step 5
Multiply the numerator by the reciprocal of the denominator.
Step 6
Combine.
Step 7
Cancel the common factor of and .
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Step 7.1
Factor out of .
Step 7.2
Cancel the common factors.
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Step 7.2.1
Factor out of .
Step 7.2.2
Cancel the common factor.
Step 7.2.3
Rewrite the expression.
Step 8
Cancel the common factor of and .
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Step 8.1
Factor out of .
Step 8.2
Cancel the common factors.
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Step 8.2.1
Multiply by .
Step 8.2.2
Cancel the common factor.
Step 8.2.3
Rewrite the expression.
Step 8.2.4
Divide by .