%5E3%2F2-simplified.jpeg "(4x^2)^3/2 Simplified")
Simplifying the Expression (4x^2)^3/2
In this article, we will simplify the expression (4x^2)^3/2. To do this, we need to follow the order of operations (PEMDAS) and apply the rules of exponents.
Step 1: Simplify the Exponentiation
First, we need to simplify the exponentiation of (4x^2)^3. To do this, we can apply the power rule of exponents, which states that (ab)^n = a^n * b^n. In this case, we have:
(4x^2)^3 = 4^3 * (x^2)^3
Step 2: Simplify the Exponents
Next, we can simplify the exponents of 4^3 and (x^2)^3. For 4^3, we have:
4^3 = 64
And for (x^2)^3, we can apply the power rule again:
(x^2)^3 = x^(2*3) = x^6
So, we have:
(4x^2)^3 = 64 * x^6
Step 3: Simplify the Fractional Exponent
Now, we need to simplify the fractional exponent of (64 * x^6)^1/2. To do this, we can apply the rule of fractional exponents, which states that a^(m/n) = nth root of a^m. In this case, we have:
(64 * x^6)^1/2 = sqrt(64 * x^6)
Step 4: Simplify the Square Root
Finally, we can simplify the square root of 64 * x^6. We know that sqrt(64) = 8, so we have:
sqrt(64 * x^6) = 8 * sqrt(x^6)
Final Answer
Therefore, the simplified expression of (4x^2)^3/2 is:
8 * sqrt(x^6)
or, in a more simplified form:
8x^3
And that's the final answer!
