Which of the following expressions is equivalent to 3√216/27^1/3 when applying the exponent properties?(1 point)
Responses
8
8
1/2
Start Fraction 1 over 2 End Fraction
2
2
18
18
The expression 3√216/27^1/3 can be simplified using the exponent properties by rewriting 216 and 27 with a common base of 3.
216 can be expressed as 6^3.
27 can be expressed as 3^3.
Therefore, the expression becomes:
3√6^3 / 3^(3/3)
Simplifying further, 3√6^3 simplifies to 3 * 6 = 18.
And 3^(3/3) simplifies to 3^1 = 3.
So the equivalent expression is 18/3, which simplifies to 6.
The correct answer is 6.
There isnt a 6 thou
Apologies for the confusion. Let's reassess the simplification:
The expression 3√216 can be simplified as follows:
3√216 = 3√(6^3)
Using the exponent property of radicals, we can rewrite it as:
3 * (6^(3/3))
Now, simplifying further, we have:
3 * (6^1) = 3 * 6 = 18
Next, let's simplify 27^(1/3):
27^(1/3) is the cubed root of 27, which is 3.
Therefore, the expression 3√216/27^(1/3) simplifies to:
18 / 3 = 6
Therefore, the correct answer is 6.
To simplify the expression 3√216/27^1/3 using exponent properties, we can rewrite the numbers as powers with the same base.
First, let's rewrite 216 and 27 in terms of their prime factorization:
216 = 2^3 * 3^3
27 = 3^3
Now, let's rewrite the expression using the exponent properties:
3√(2^3 * 3^3) / (3^3)^1/3
Since the exponent 1/3 in the denominator means taking the cube root, we can simplify further:
3√(2^3 * 3^3) / 3^(3 * 1/3)
Next, simplify the cube root and the exponent in the denominator:
2 * 3 / 3^(3 * 1/3)
Since 3 * 1/3 is equal to 1, we have:
2 * 3 / 3^1
Finally, simplify the expression:
6 / 3
This is equivalent to 2.
Therefore, the correct answer is 2.