%5E2*(5x%5E2y%5E6)-(7x%5E5y%5E4)%5E2.jpeg "(-3x^4y)^2*(5x^2y^6)-(7x^5y^4)^2")
Simplifying the Expression (-3x^4y)^2*(5x^2y^6)-(7x^5y^4)^2
This expression involves simplifying a combination of multiplications and exponents. Let's break down the steps to solve it.
Step 1: Apply the Exponent Rule
We'll start by applying the rule of exponents which states that (ab)^n = a^n * b^n. This allows us to distribute the exponent to each term inside the parentheses.
- (-3x^4y)^2 = (-3)^2 * (x^4)^2 * (y)^2 = 9x^8y^2
- (7x^5y^4)^2 = (7)^2 * (x^5)^2 * (y^4)^2 = 49x^10y^8
Step 2: Substitute Simplified Terms
Now, let's substitute these simplified terms back into the original expression:
- 9x^8y^2 * (5x^2y^6) - 49x^10y^8
Step 3: Multiply the Remaining Terms
Next, we multiply the coefficients and combine the variables using the rule x^m * x^n = x^(m+n).
- 45x^10y^8 - 49x^10y^8
Step 4: Combine Like Terms
Finally, we combine the like terms, which are the terms with the same variables and exponents.
- -4x^10y^8
Conclusion
Therefore, the simplified form of the expression (-3x^4y)^2*(5x^2y^6)-(7x^5y^4)^2 is -4x^10y^8.