# Solve for n (1/8)^(3-n)*4=4 (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
Multiply the exponents in (23)-(3-n).
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
Solve for n.
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

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