12square root(-10)^12
12 * (-10)^6
= 12 * 10^6
because negative number to an even power is positive
Where does the 6 come from?
To simplify the expression 12 * √(-10)^12, we first need to simplify the square root of -10 raised to the power of 12.
The square root of a negative number is not defined in the realm of real numbers. However, it is defined in the realm of complex numbers.
To simplify the square root of -10 raised to the power of 12, we focus on the real part, ignoring the square root. Let's break it down step by step:
Step 1: Simplify the square root of -10.
√(-10) = √(-1 * 10) = √(-1) * √(10) = i * √(10) (using the property of square roots)
Step 2: Raise the simplified square root to the power of 12.
(i * √(10))^12 = i^12 * (√(10))^12 = i^12 * 10^6 (using the property of exponents)
Note that i is the imaginary unit, where i^2 = -1.
Step 3: Simplify i^12.
To simplify i^12, we observe that i^4 = (i^2)^2 = (-1)^2 = 1.
Therefore, i^12 = (i^4)^3 = 1^3 = 1.
Step 4: Substitute the simplified values back into the original expression.
12 * √(-10)^12 = 12 * (i^12 * 10^6) = 12 * 1 * 10^6 = 12 * 10^6 = 12,000,000.
So, the simplified value of 12 * √(-10)^12 is 12,000,000.