(18)3-n⋅4=4

Apply the product rule to 18.

13-n83-n⋅4=4

One to any power is one.

183-n⋅4=4

Move 83-n to the numerator using the negative exponent rule 1b-n=bn.

8-(3-n)⋅4=4

Rewrite 8 as 23.

(23)-(3-n)⋅4=4

Apply the power rule and multiply exponents, (am)n=amn.

23(-(3-n))⋅4=4

Apply the distributive property.

23(-1⋅3–n)⋅4=4

Multiply -1 by 3.

23(-3–n)⋅4=4

Multiply –n.

Multiply -1 by -1.

23(-3+1n)⋅4=4

Multiply n by 1.

23(-3+n)⋅4=4

23(-3+n)⋅4=4

Apply the distributive property.

23⋅-3+3n⋅4=4

Multiply 3 by -3.

2-9+3n⋅4=4

2-9+3n⋅4=4

Rewrite 4 as 22.

2-9+3n⋅22=4

Use the power rule aman=am+n to combine exponents.

2-9+3n+2=4

Add -9 and 2.

23n-7=4

Create equivalent expressions in the equation that all have equal bases.

23n-7=22

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

3n-7=2

Move all terms not containing n to the right side of the equation.

Add 7 to both sides of the equation.

3n=2+7

Add 2 and 7.

3n=9

3n=9

Divide each term by 3 and simplify.

Divide each term in 3n=9 by 3.

3n3=93

Cancel the common factor of 3.

Cancel the common factor.

3n3=93

Divide n by 1.

n=93

n=93

Divide 9 by 3.

n=3

n=3

n=3

Solve for n (1/8)^(3-n)*4=4