27n+3⋅9n+43n+1⋅81n+2

Rewrite 27 as 33.

(33)n+3⋅9n+43n+1⋅81n+2

Multiply the exponents in (33)n+3.

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.

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

Rewrite 81 as 34.

35n+173n+1⋅(34)n+2

Multiply the exponents in (34)n+2.

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

Cancel the common factor of 35n+17 and 35n+9.

Factor 35n+9 out of 35n+17.

35n+9⋅35n+17-(5n+9)35n+9

Cancel the common factors.

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.

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.

Combine the opposite terms in 5n+17-5n-9.

Subtract 5n from 5n.

30+17-9

Add 0 and 17.

317-9

317-9

Simplify the expression.

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))