Problem

Simplify the exponential expression. \[ \frac{-6 x^{7} y^{7}}{2 x^{4} y^{3}} \] $\frac{-6 x^{7} y^{7}}{2 x^{4} y^{3}}=\square$ (Simplify your answer. Use positive exponents only.)

Solution

Step 1 :The given expression is a fraction with both the numerator and denominator having similar terms. The terms in the numerator and denominator can be simplified by dividing each term in the numerator by each corresponding term in the denominator.

Step 2 :The rules of exponents state that when dividing like bases, the exponents should be subtracted. Therefore, the exponent of x in the numerator (7) should be subtracted from the exponent of x in the denominator (4) and the exponent of y in the numerator (7) should be subtracted from the exponent of y in the denominator (3).

Step 3 :Also, -6 divided by 2 gives -3.

Step 4 :So, the new coefficient is -3, the new exponent of x is 3, and the new exponent of y is 4.

Step 5 :Final Answer: The simplified form of the given expression is \(\boxed{-3x^{3}y^{4}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/U7rX0BF4Wq/

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