Which of the expression below is equivalent to the following expression 5 square root of (n + 4)^3? Chose the correct one and explain your answer.

Question

Which of the expression below is equivalent to the following expression 5 square root of (n + 4)^3? Chose the correct one and explain your answer.

a) (n+ 4) ^5
b) (n + 4) 1/5
c) (n + 4) 5/3
d) (n 4) 3/5

Answer 1

The correct answer is c) (n + 4)^(5/3).

To simplify the expression 5√((n + 4)^3), we first need to apply the power rule: (a^m)^n = a^(m * n).

So, (n + 4)^3 can be written as [(n + 4)^(3/1)], which simplifies to (n + 4)^(3).

Next, we can use the exponentiation rule: √(a^m) = a^(m/n).

Therefore, 5√((n + 4)^3) becomes [5 * (n + 4)^(3/1)]^(1/5).

Using the power rule again, we can simplify this to [(5^(1/5)) * (n + 4)^(3/1)].

Finally, we can simplify 5^(1/5) to 1, as the fifth root of 5 is 1. So, the expression becomes (n + 4)^(3/1), which is equivalent to (n + 4)^(3).

The expression (n + 4)^(5/3) is the same as (n + 4)^(3), so the correct answer is c) (n + 4)^(5/3).