Simplify (27^(n+3)*9^(n+4))/(3^(n+1)*81^(n+2))

Math
27n+3⋅9n+43n+1⋅81n+2
Simplify the numerator.
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Rewrite 27 as 33.
(33)n+3⋅9n+43n+1⋅81n+2
Multiply the exponents in (33)n+3.
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Apply the power rule and multiply exponents, (am)n=amn.
33(n+3)⋅9n+43n+1⋅81n+2
Apply the distributive property.
33n+3⋅3⋅9n+43n+1⋅81n+2
Multiply 3 by 3.
33n+9⋅9n+43n+1⋅81n+2
33n+9⋅9n+43n+1⋅81n+2
Rewrite 9 as 32.
33n+9⋅(32)n+43n+1⋅81n+2
Multiply the exponents in (32)n+4.
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Apply the power rule and multiply exponents, (am)n=amn.
33n+9⋅32(n+4)3n+1⋅81n+2
Apply the distributive property.
33n+9⋅32n+2⋅43n+1⋅81n+2
Multiply 2 by 4.
33n+9⋅32n+83n+1⋅81n+2
33n+9⋅32n+83n+1⋅81n+2
Use the power rule aman=am+n to combine exponents.
33n+9+2n+83n+1⋅81n+2
Add 3n and 2n.
35n+9+83n+1⋅81n+2
Add 9 and 8.
35n+173n+1⋅81n+2
35n+173n+1⋅81n+2
Simplify the denominator.
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Rewrite 81 as 34.
35n+173n+1⋅(34)n+2
Multiply the exponents in (34)n+2.
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Apply the power rule and multiply exponents, (am)n=amn.
35n+173n+1⋅34(n+2)
Apply the distributive property.
35n+173n+1⋅34n+4⋅2
Multiply 4 by 2.
35n+173n+1⋅34n+8
35n+173n+1⋅34n+8
Use the power rule aman=am+n to combine exponents.
35n+173n+1+4n+8
Add n and 4n.
35n+1735n+1+8
Add 1 and 8.
35n+1735n+9
35n+1735n+9
Simplify terms.
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Cancel the common factor of 35n+17 and 35n+9.
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Factor 35n+9 out of 35n+17.
35n+9⋅35n+17-(5n+9)35n+9
Cancel the common factors.
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Multiply by 1.
35n+9⋅35n+17-(5n+9)35n+9⋅1
Cancel the common factor.
35n+9⋅35n+17-(5n+9)35n+9⋅1
Rewrite the expression.
35n+17-(5n+9)1
Divide 35n+17-(5n+9) by 1.
35n+17-(5n+9)
35n+17-(5n+9)
35n+17-(5n+9)
Simplify each term.
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Apply the distributive property.
35n+17-(5n)-1⋅9
Multiply 5 by -1.
35n+17-5n-1⋅9
Multiply -1 by 9.
35n+17-5n-9
35n+17-5n-9
Simplify by adding terms.
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Combine the opposite terms in 5n+17-5n-9.
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Subtract 5n from 5n.
30+17-9
Add 0 and 17.
317-9
317-9
Simplify the expression.
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Subtract 9 from 17.
38
Raise 3 to the power of 8.
6561
6561
6561
6561
Simplify (27^(n+3)*9^(n+4))/(3^(n+1)*81^(n+2))

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