Basic Math Examples

Simplify (5ab+2a(2b))^3+(1/3*(ab))^2(ab)+3/2*(a^2b(1/3*(ab^2)))-1/9*(a^3b^3)
Step 1
Simplify each term.
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Step 1.1
Simplify each term.
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Step 1.1.1
Rewrite using the commutative property of multiplication.
Step 1.1.2
Multiply by .
Step 1.2
Add and .
Step 1.3
Use the power rule to distribute the exponent.
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Step 1.3.1
Apply the product rule to .
Step 1.3.2
Apply the product rule to .
Step 1.4
Raise to the power of .
Step 1.5
Multiply .
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Step 1.5.1
Combine and .
Step 1.5.2
Combine and .
Step 1.6
Use the power rule to distribute the exponent.
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Step 1.6.1
Apply the product rule to .
Step 1.6.2
Apply the product rule to .
Step 1.7
Raise to the power of .
Step 1.8
Multiply .
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Step 1.8.1
Combine and .
Step 1.8.2
Raise to the power of .
Step 1.8.3
Use the power rule to combine exponents.
Step 1.8.4
Add and .
Step 1.8.5
Combine and .
Step 1.8.6
Raise to the power of .
Step 1.8.7
Use the power rule to combine exponents.
Step 1.8.8
Add and .
Step 1.9
Multiply by by adding the exponents.
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Step 1.9.1
Move .
Step 1.9.2
Multiply by .
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Step 1.9.2.1
Raise to the power of .
Step 1.9.2.2
Use the power rule to combine exponents.
Step 1.9.3
Add and .
Step 1.10
Multiply by by adding the exponents.
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Step 1.10.1
Move .
Step 1.10.2
Multiply by .
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Step 1.10.2.1
Raise to the power of .
Step 1.10.2.2
Use the power rule to combine exponents.
Step 1.10.3
Add and .
Step 1.11
Multiply .
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Step 1.11.1
Combine and .
Step 1.11.2
Combine and .
Step 1.12
Combine.
Step 1.13
Cancel the common factor of .
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Step 1.13.1
Cancel the common factor.
Step 1.13.2
Rewrite the expression.
Step 1.14
Multiply .
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Step 1.14.1
Combine and .
Step 1.14.2
Combine and .
Step 2
Simplify terms.
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Step 2.1
Combine the numerators over the common denominator.
Step 2.2
Combine the opposite terms in .
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Step 2.2.1
Reorder the factors in the terms and .
Step 2.2.2
Subtract from .
Step 2.3
Combine the opposite terms in .
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Step 2.3.1
Divide by .
Step 2.3.2
Add and .
Step 3
Combine and using a common denominator.
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Step 3.1
Reorder and .
Step 3.2
To write as a fraction with a common denominator, multiply by .
Step 3.3
Combine and .
Step 3.4
Combine the numerators over the common denominator.
Step 4
Simplify the numerator.
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Step 4.1
Factor out of .
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Step 4.1.1
Factor out of .
Step 4.1.2
Factor out of .
Step 4.1.3
Factor out of .
Step 4.2
Multiply by .
Step 4.3
Add and .
Step 5
Move to the left of .