Basic Math Examples

Simplify (p^(-1/4)q^(-3/2))/((3^-1p^-2q^(-2/3))^-2)
Step 1
Simplify the expression.
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Step 1.1
Move to the denominator using the negative exponent rule .
Step 1.2
Move to the denominator using the negative exponent rule .
Step 1.3
Move to the numerator using the negative exponent rule .
Step 2
Simplify the numerator.
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Step 2.1
Apply the product rule to .
Step 2.2
Rewrite the expression using the negative exponent rule .
Step 2.3
Rewrite the expression using the negative exponent rule .
Step 2.4
Combine.
Step 2.5
Multiply by .
Step 2.6
Use the power rule to distribute the exponent.
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Step 2.6.1
Apply the product rule to .
Step 2.6.2
Apply the product rule to .
Step 2.7
One to any power is one.
Step 2.8
Simplify the denominator.
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Step 2.8.1
Raise to the power of .
Step 2.8.2
Multiply the exponents in .
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Step 2.8.2.1
Apply the power rule and multiply exponents, .
Step 2.8.2.2
Multiply by .
Step 2.9
Multiply the exponents in .
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Step 2.9.1
Apply the power rule and multiply exponents, .
Step 2.9.2
Multiply .
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Step 2.9.2.1
Multiply by .
Step 2.9.2.2
Combine and .
Step 2.9.2.3
Multiply by .
Step 2.9.3
Move the negative in front of the fraction.
Step 2.10
Rewrite the expression using the negative exponent rule .
Step 3
Multiply by .
Step 4
Multiply the numerator by the reciprocal of the denominator.
Step 5
Combine.
Step 6
Multiply by by adding the exponents.
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Step 6.1
Move .
Step 6.2
Use the power rule to combine exponents.
Step 6.3
To write as a fraction with a common denominator, multiply by .
Step 6.4
Combine and .
Step 6.5
Combine the numerators over the common denominator.
Step 6.6
Simplify the numerator.
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Step 6.6.1
Multiply by .
Step 6.6.2
Add and .
Step 7
Multiply by by adding the exponents.
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Step 7.1
Move .
Step 7.2
Use the power rule to combine exponents.
Step 7.3
To write as a fraction with a common denominator, multiply by .
Step 7.4
To write as a fraction with a common denominator, multiply by .
Step 7.5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 7.5.1
Multiply by .
Step 7.5.2
Multiply by .
Step 7.5.3
Multiply by .
Step 7.5.4
Multiply by .
Step 7.6
Combine the numerators over the common denominator.
Step 7.7
Simplify the numerator.
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Step 7.7.1
Multiply by .
Step 7.7.2
Multiply by .
Step 7.7.3
Add and .
Step 8
Multiply by .