Simplify:-
3√-108a^4 b^3
Hmmm. I assume you mean
∛(-108a^4 b^3)
=∛((-3^3*4)*(a^3*a)*b^3)
= -3ab∛(4a)
To simplify the expression 3√(-108a^4b^3), we can begin by simplifying the cube root.
Step 1: Simplify the cube root
Since the cube root of a negative number is not real, we can rewrite -108 as -1 * 3^3 * 2^3. Rewriting the expression, we have:
3√(-108a^4b^3) = 3√(-1 * 3^3 * 2^3 * a^4 * b^3)
Next, we can simplify the cube root of the perfect cubes:
3√(-1 * 3^3 * 2^3 * a^4 * b^3) = -3 * 2 * a * b * 3√(a)
Step 2: Simplify the remaining terms
The remaining terms without a cube root are -3 * 2 * a * b. Multiplying these terms together, we have:
-3 * 2 * a * b = -6ab
Putting it all together, the simplified expression is:
-6ab * 3√(a)
Therefore, the simplified form of 3√(-108a^4b^3) is -6ab * 3√(a).
To simplify the expression 3√(-108a^4b^3), we will start by breaking down the expression.
Step 1: Find the factors inside the cube root (√).
-108 has factors of -1, 2, 2, 3, 3, 3, which can be written as -1 * 2 * 2 * 3 * 3 * 3.
a^4 can be written as a * a * a * a.
b^3 can be written as b * b * b.
Step 2: Rearrange the factors.
We can group the factors into pairs of three to be taken out of the cube root. Since the cube root of a product equals the product of the cube roots, we have:
3√[(-1 * 2 * 2 * 3 * 3 * 3) * (a * a * a * a * b * b * b)].
Step 3: Simplify the cube root of each factor.
The cube root of -1 * 2 * 2 * 3 * 3 * 3 is -6, as -6 * -6 * -6 = -216.
The cube root of a * a * a * a is a^3.
The cube root of b * b * b is b^3.
So, the simplified expression is:
-6a^3b^3