Simplify: (-1728)^1/3
My answer was -576...is this correct?
Ktdydyo
Yes, your answer of -576 is correct. The expression (-1728)^(1/3) means finding the cube root of -1728. The cube root of a number is the value that, when raised to the exponent of 3, equals the original number. In this case, -576^3 equals -1728.
To simplify the expression (-1728)^(1/3), you need to find the cube root of -1728.
First, let's determine the cube root of 1728. Since 12^3 is equal to 1728, the cube root of 1728 is 12.
Now let's consider the negative sign. Since we have (-1728)^(1/3), the cube root is raised to the power of 1/3. Since the exponent is odd (in this case, 1/3), the negative sign remains.
Therefore, the simplified expression is -12.
So, the correct answer is -12, not -576.
( -1728 ) ^ ( 1 / 3 ) = third root of ( - 1728 ) =
third root of ( - 1 ) * third root of ( 1728 ) =
- 1 * 12 = - 12