4.jpeg "(-3ab3)4")
Simplifying (-3ab3)4
This expression involves raising a product with a negative coefficient and exponents to another power. Let's break down the steps to simplify it:
Understanding the Properties
- Exponent of a product: (xy)ⁿ = xⁿyⁿ
- Exponent of a power: (xⁿ)ᵐ = xⁿᵐ
- Negative base raised to an even exponent: (-x)<sup>2n</sup> = x<sup>2n</sup>
Applying the Properties
-
Apply the exponent of a product property: (-3ab<sup>3</sup>)<sup>4</sup> = (-3)<sup>4</sup> * a<sup>4</sup> * (b<sup>3</sup>)<sup>4</sup>
-
Apply the exponent of a power property: (-3)<sup>4</sup> * a<sup>4</sup> * (b<sup>3</sup>)<sup>4</sup> = 81 * a<sup>4</sup> * b<sup>12</sup>
Final Result
Therefore, the simplified form of (-3ab<sup>3</sup>)<sup>4</sup> is 81a<sup>4</sup>b<sup>12</sup>.