Pre-Algebra Examples

Multiply (2/3m^2-5n^3-3/8p^4)^2
Step 1
Simplify terms.
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Step 1.1
Simplify each term.
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Step 1.1.1
Combine and .
Step 1.1.2
Combine and .
Step 1.1.3
Move to the left of .
Step 1.2
Rewrite as .
Step 2
Expand by multiplying each term in the first expression by each term in the second expression.
Step 3
Simplify terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Combine.
Step 3.1.2
Multiply by by adding the exponents.
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Step 3.1.2.1
Move .
Step 3.1.2.2
Use the power rule to combine exponents.
Step 3.1.2.3
Add and .
Step 3.1.3
Multiply by .
Step 3.1.4
Multiply by .
Step 3.1.5
Rewrite using the commutative property of multiplication.
Step 3.1.6
Multiply .
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Step 3.1.6.1
Combine and .
Step 3.1.6.2
Multiply by .
Step 3.1.7
Move the negative in front of the fraction.
Step 3.1.8
Combine and .
Step 3.1.9
Move to the left of .
Step 3.1.10
Rewrite using the commutative property of multiplication.
Step 3.1.11
Cancel the common factor of .
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Step 3.1.11.1
Move the leading negative in into the numerator.
Step 3.1.11.2
Factor out of .
Step 3.1.11.3
Factor out of .
Step 3.1.11.4
Cancel the common factor.
Step 3.1.11.5
Rewrite the expression.
Step 3.1.12
Cancel the common factor of .
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Step 3.1.12.1
Factor out of .
Step 3.1.12.2
Cancel the common factor.
Step 3.1.12.3
Rewrite the expression.
Step 3.1.13
Combine and .
Step 3.1.14
Multiply .
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Step 3.1.14.1
Combine and .
Step 3.1.14.2
Multiply by .
Step 3.1.14.3
Combine and .
Step 3.1.15
Remove unnecessary parentheses.
Step 3.1.16
Move to the left of .
Step 3.1.17
Move the negative in front of the fraction.
Step 3.1.18
Rewrite using the commutative property of multiplication.
Step 3.1.19
Multiply by by adding the exponents.
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Step 3.1.19.1
Move .
Step 3.1.19.2
Use the power rule to combine exponents.
Step 3.1.19.3
Add and .
Step 3.1.20
Multiply by .
Step 3.1.21
Multiply .
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Step 3.1.21.1
Multiply by .
Step 3.1.21.2
Combine and .
Step 3.1.21.3
Multiply by .
Step 3.1.21.4
Combine and .
Step 3.1.22
Move to the left of .
Step 3.1.23
Cancel the common factor of .
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Step 3.1.23.1
Move the leading negative in into the numerator.
Step 3.1.23.2
Factor out of .
Step 3.1.23.3
Cancel the common factor.
Step 3.1.23.4
Rewrite the expression.
Step 3.1.24
Cancel the common factor of .
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Step 3.1.24.1
Factor out of .
Step 3.1.24.2
Factor out of .
Step 3.1.24.3
Cancel the common factor.
Step 3.1.24.4
Rewrite the expression.
Step 3.1.25
Combine and .
Step 3.1.26
Move the negative in front of the fraction.
Step 3.1.27
Multiply .
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Step 3.1.27.1
Multiply by .
Step 3.1.27.2
Combine and .
Step 3.1.27.3
Multiply by .
Step 3.1.27.4
Combine and .
Step 3.1.28
Multiply .
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Step 3.1.28.1
Multiply by .
Step 3.1.28.2
Multiply by .
Step 3.1.28.3
Multiply by .
Step 3.1.28.4
Multiply by .
Step 3.1.28.5
Multiply by by adding the exponents.
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Step 3.1.28.5.1
Move .
Step 3.1.28.5.2
Use the power rule to combine exponents.
Step 3.1.28.5.3
Add and .
Step 3.1.28.6
Multiply by .
Step 3.2
Simplify terms.
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Step 3.2.1
Combine the numerators over the common denominator.
Step 3.2.2
Subtract from .
Step 3.2.3
Subtract from .
Step 4
Add and .
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Step 4.1
Move .
Step 4.2
Add and .
Step 5
Simplify each term.
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Step 5.1
Move the negative in front of the fraction.
Step 5.2
Cancel the common factor of and .
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Step 5.2.1
Factor out of .
Step 5.2.2
Cancel the common factors.
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Step 5.2.2.1
Factor out of .
Step 5.2.2.2
Cancel the common factor.
Step 5.2.2.3
Rewrite the expression.
Step 5.3
Move the negative in front of the fraction.
Step 5.4
Cancel the common factor of and .
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Step 5.4.1
Factor out of .
Step 5.4.2
Cancel the common factors.
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Step 5.4.2.1
Factor out of .
Step 5.4.2.2
Cancel the common factor.
Step 5.4.2.3
Rewrite the expression.
Step 6
Simplify the expression.
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Step 6.1
Move .
Step 6.2
Reorder and .
Step 6.3
Move .
Step 6.4
Move .
Step 6.5
Move .
Step 6.6
Move .
Step 6.7
Reorder and .