(-2a%5E3b).jpeg "(5a^6b^-4)(-2a^3b)")
Simplifying Expressions with Exponents
This article will guide you through the process of simplifying the expression (5a^6b^-4)(-2a^3b). We will break down the steps involved using the rules of exponents.
Understanding the Rules
To simplify expressions with exponents, we need to recall the following key rules:
- Product of Powers: When multiplying powers with the same base, add the exponents. a^m * a^n = a^(m+n)
- Quotient of Powers: When dividing powers with the same base, subtract the exponents. a^m / a^n = a^(m-n)
- Power of a Power: When raising a power to another power, multiply the exponents. (a^m)^n = a^(mn)*
- Negative Exponent: Any base raised to a negative exponent is equal to its reciprocal raised to the positive exponent. a^-n = 1/a^n
Simplifying the Expression
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Apply the Product of Powers Rule:
- (5a^6b^-4)(-2a^3b) = (5 * -2) * (a^6 * a^3) * (b^-4 * b)
- = -10 * a^(6+3) * b^(-4+1)
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Simplify the exponents:
- = -10a^9b^-3
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Apply the Negative Exponent Rule:
- = -10a^9 * (1/b^3)
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Combine the terms:
- = -10a^9 / b^3
Conclusion
Therefore, the simplified form of the expression (5a^6b^-4)(-2a^3b) is -10a^9 / b^3. Understanding the rules of exponents allows us to efficiently manipulate expressions and simplify them to their most basic form.