Precalculus Examples

Simplify ((xy^-2z^-3)/(2x^-2yz^2))^-3
Step 1
Move to the denominator using the negative exponent rule .
Step 2
Move to the denominator using the negative exponent rule .
Step 3
Simplify the denominator.
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Step 3.1
Multiply by by adding the exponents.
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Step 3.1.1
Move .
Step 3.1.2
Multiply by .
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Step 3.1.2.1
Raise to the power of .
Step 3.1.2.2
Use the power rule to combine exponents.
Step 3.1.3
Add and .
Step 3.2
Multiply by by adding the exponents.
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Step 3.2.1
Move .
Step 3.2.2
Use the power rule to combine exponents.
Step 3.2.3
Add and .
Step 4
Move to the numerator using the negative exponent rule .
Step 5
Multiply by by adding the exponents.
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Step 5.1
Multiply by .
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Step 5.1.1
Raise to the power of .
Step 5.1.2
Use the power rule to combine exponents.
Step 5.2
Add and .
Step 6
Change the sign of the exponent by rewriting the base as its reciprocal.
Step 7
Use the power rule to distribute the exponent.
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Step 7.1
Apply the product rule to .
Step 7.2
Apply the product rule to .
Step 7.3
Apply the product rule to .
Step 8
Simplify the numerator.
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Step 8.1
Raise to the power of .
Step 8.2
Multiply the exponents in .
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Step 8.2.1
Apply the power rule and multiply exponents, .
Step 8.2.2
Multiply by .
Step 8.3
Multiply the exponents in .
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Step 8.3.1
Apply the power rule and multiply exponents, .
Step 8.3.2
Multiply by .
Step 9
Multiply the exponents in .
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Step 9.1
Apply the power rule and multiply exponents, .
Step 9.2
Multiply by .