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Q10: Find the simplified form of the expression.
((3)/(6n^(4)))^(3)

Answer 1

To simplify the expression ((3)/(6n^(4)))^(3), we start by simplifying the numerator and denominator separately:

Numerator: 3
Denominator: 6n^4

Since 3 is already simplified, we can focus on simplifying the denominator:

6n^4 can be rewritten as (2 * 3 * n^4).
Since 2 and 3 are both divisible by 3, we can simplify to (1/3 * 2 * n^4).

Now we can rewrite the original expression using the simplified numerator and denominator:

((3)/(6n^(4)))^(3) = ((1/3 * 2 * n^4)^(3)

Next, we simplify the exponent by raising each term inside the parentheses to the 3rd power:

((1/3 * 2 * n^4)^(3)) = ((1/3)^3 * (2)^3 * (n^4)^3)

Simplifying each term raised to the 3rd power:

((1/3)^3 = (1^3)/(3^3) = 1/27
(2)^3 = 2 * 2 * 2 = 8
(n^4)^3 = n^(4*3) = n^12

Now we can rewrite the expression using the simplified terms:

((1/3)^3 * (2)^3 * (n^4)^3) = (1/27) * 8 * n^12

Finally, we simplify the expression:

(1/27) * 8 * n^12 = (8/27) * n^12

Therefore, the simplified form of the expression ((3)/(6n^(4)))^(3) is (8/27) * n^12.