Basic Math Examples

Simplify ((7p^2q^4)/(8r^2s^3))^3*((12p^5s^7)/(21p^5q^3s^4))^3
Step 1
Use the power rule to distribute the exponent.
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Step 1.1
Apply the product rule to .
Step 1.2
Apply the product rule to .
Step 1.3
Apply the product rule to .
Step 1.4
Apply the product rule to .
Step 1.5
Apply the product rule to .
Step 2
Simplify the numerator.
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Step 2.1
Raise to the power of .
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 3
Simplify the denominator.
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Step 3.1
Raise to the power of .
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
Multiply the exponents in .
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Step 3.3.1
Apply the power rule and multiply exponents, .
Step 3.3.2
Multiply by .
Step 4
Reduce the expression by cancelling the common factors.
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Step 4.1
Cancel the common factor of and .
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Step 4.1.1
Factor out of .
Step 4.1.2
Cancel the common factors.
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Step 4.1.2.1
Factor out of .
Step 4.1.2.2
Cancel the common factor.
Step 4.1.2.3
Rewrite the expression.
Step 4.2
Cancel the common factor of .
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Step 4.2.1
Cancel the common factor.
Step 4.2.2
Rewrite the expression.
Step 4.3
Cancel the common factor of and .
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Step 4.3.1
Factor out of .
Step 4.3.2
Cancel the common factors.
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Step 4.3.2.1
Factor out of .
Step 4.3.2.2
Cancel the common factor.
Step 4.3.2.3
Rewrite the expression.
Step 5
Use the power rule to distribute the exponent.
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Step 5.1
Apply the product rule to .
Step 5.2
Apply the product rule to .
Step 5.3
Apply the product rule to .
Step 6
Combine.
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 7.3
Multiply by .
Step 8
Simplify the denominator.
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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 by .
Step 9
Reduce the expression by cancelling the common factors.
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Step 9.1
Cancel the common factor of and .
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Step 9.1.1
Factor out of .
Step 9.1.2
Cancel the common factors.
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Step 9.1.2.1
Factor out of .
Step 9.1.2.2
Cancel the common factor.
Step 9.1.2.3
Rewrite the expression.
Step 9.2
Cancel the common factor of and .
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Step 9.2.1
Factor out of .
Step 9.2.2
Cancel the common factors.
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Step 9.2.2.1
Factor out of .
Step 9.2.2.2
Cancel the common factor.
Step 9.2.2.3
Rewrite the expression.
Step 9.3
Cancel the common factor of .
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Step 9.3.1
Cancel the common factor.
Step 9.3.2
Rewrite the expression.