Pre-Algebra Examples

Simplify ((m^2n^-3)/(3n^4m^-2))^-3((6p^3)/(3p^3n^-5))^-2
Step 1
Move to the denominator using the negative exponent rule .
Step 2
Multiply by by adding the exponents.
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Step 2.1
Move .
Step 2.2
Use the power rule to combine exponents.
Step 2.3
Add and .
Step 3
Move to the numerator using the negative exponent rule .
Step 4
Multiply by by adding the exponents.
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Step 4.1
Use the power rule to combine exponents.
Step 4.2
Add and .
Step 5
Change the sign of the exponent by rewriting the base as its reciprocal.
Step 6
Use the power rule to distribute the exponent.
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Step 6.1
Apply the product rule to .
Step 6.2
Apply the product rule to .
Step 7
Simplify the numerator.
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Step 7.1
Raise to the power of .
Step 7.2
Multiply the exponents in .
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Step 7.2.1
Apply the power rule and multiply exponents, .
Step 7.2.2
Multiply by .
Step 8
Reduce the expression by cancelling the common factors.
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Step 8.1
Multiply the exponents in .
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Step 8.1.1
Apply the power rule and multiply exponents, .
Step 8.1.2
Multiply by .
Step 8.2
Move to the numerator using the negative exponent rule .
Step 8.3
Cancel the common factor of and .
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Step 8.3.1
Factor out of .
Step 8.3.2
Cancel the common factors.
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Step 8.3.2.1
Factor out of .
Step 8.3.2.2
Cancel the common factor.
Step 8.3.2.3
Rewrite the expression.
Step 8.4
Cancel the common factor of .
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Step 8.4.1
Cancel the common factor.
Step 8.4.2
Divide by .
Step 9
Rewrite the expression using the negative exponent rule .
Step 10
Combine fractions.
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Step 10.1
Combine.
Step 10.2
Multiply by .
Step 11
Simplify the denominator.
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Step 11.1
Apply the product rule to .
Step 11.2
Raise to the power of .
Step 11.3
Multiply the exponents in .
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Step 11.3.1
Apply the power rule and multiply exponents, .
Step 11.3.2
Multiply by .
Step 12
Reduce the expression by cancelling the common factors.
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Step 12.1
Cancel the common factor of and .
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Step 12.1.1
Factor out of .
Step 12.1.2
Cancel the common factors.
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Step 12.1.2.1
Factor out of .
Step 12.1.2.2
Cancel the common factor.
Step 12.1.2.3
Rewrite the expression.
Step 12.2
Move to the left of .