(3 to the power of divided by 3 root 27 =3 to the power n+2,find the value of n
Answers
Answer:
Let’s start with the 27, which = 3*3*3 = 3^3. When we take a square root of that, it is equivalent to dividing the power (3) by 2 (3/2 = 1.5). A square root of a number is that number raised to the power of 1/2 or 0.5. A power raised to a power means multiplication of powers. Therefore, SQRT(27) = 3^1.5.
When we multiply this by 3, it means adding 1 to the power (1.5) because 3 = 3^1 (1.5+1 = 2.5). A multiplication of the same numbers is equivalent to the addition of the powers. Therefore, on the left side we have 3^2.5.
Since on the right side we see 3^n, we can conclude that n = 2.5.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let’s start with the 27, which = 3*3*3 = 3^3. When we take a square root of that, it is equivalent to dividing the power (3) by 2 (3/2 = 1.5). A square root of a number is that number raised to the power of 1/2 or 0.5. A power raised to a power means multiplication of powers. Therefore, SQRT(27) = 3^1.5.
When we multiply this by 3, it means adding 1 to the power (1.5) because 3 = 3^1 (1.5+1 = 2.5). A multiplication of the same numbers is equivalent to the addition of the powers. Therefore, on the left side we have 3^2.5.
Since on the right side we see 3^n, we can conclude that n = 2.5.