(a%5E3b%5E2c)(3ab%5E4c%5E5).jpeg "(-4a^3bc^2)(a^3b^2c)(3ab^4c^5)")
Simplifying Expressions with Exponents: A Step-by-Step Guide
In mathematics, simplifying expressions with exponents involves combining like terms and applying the rules of exponents. Let's explore how to simplify the expression (-4a^3bc^2)(a^3b^2c)(3ab^4c^5).
1. Rearranging the Expression
To simplify the expression, we rearrange it to group the numerical coefficients and variables with the same base together:
(-4a^3bc^2)(a^3b^2c)(3ab^4c^5) = -4 * 3 * a^3 * a^3 * a * b * b^2 * b^4 * c^2 * c * c^5
2. Applying the Rules of Exponents
Now we can apply the rules of exponents to simplify the expression:
- Product of powers: When multiplying powers with the same base, add the exponents: a^m * a^n = a^(m+n)
Applying this rule, we get:
-4 * 3 * a^3 * a^3 * a * b * b^2 * b^4 * c^2 * c * c^5 = -12 * a^(3+3+1) * b^(1+2+4) * c^(2+1+5)
3. Simplifying the Expression
Simplifying the exponents, we get:
-12 * a^(3+3+1) * b^(1+2+4) * c^(2+1+5) = **-12a^7b^7c^8**
Therefore, the simplified form of the expression (-4a^3bc^2)(a^3b^2c)(3ab^4c^5) is -12a^7b^7c^8.
This process demonstrates the power of applying the rules of exponents to simplify complex expressions.