What is the correct simplification of 243^3/5
?(1 point)
Responses
9
9
81
81
27
27
3
The correct simplification of 243^(3/5) is 27.
To simplify 243^(3/5), we need to find the fifth root of 243 and then raise it to the power of 3.
First, find the fifth root of 243:
∛243 = 3
Next, raise this result to the power of 3:
3^3 = 27
Therefore, the correct simplification of 243^(3/5) is 27.
To simplify the expression 243^(3/5), we need to apply the exponent rule for fractional exponents.
The rule states that taking the nth root of a raised to the power of m is equivalent to raising the nth root of a to the power of m. In other words, (a^m)^(1/n) = a^(m/n).
In this case, we have 243^(3/5), which means we need to find the fifth root of 243 and then raise it to the power of 3.
To find the fifth root of 243, we can take the number 243 and raise it to the power of 1/5:
243^(1/5) ≈ 3
Now that we have the fifth root of 243, we can raise it to the power of 3:
3^3 = 27
Therefore, the correct simplification of 243^(3/5) is 27.
So, the correct answer is 27.