%5E-2.jpeg "(5a^3b^4)^-2")
Simplifying Expressions with Negative Exponents: (5a³b⁴)⁻²
This article will guide you through simplifying the expression (5a³b⁴)⁻². Understanding negative exponents is crucial in algebra, and this example provides a clear illustration of how to handle them.
Understanding Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. In simpler terms:
x⁻ⁿ = 1/xⁿ
Applying the Rule to Our Expression
Let's break down the simplification process step-by-step:
-
Distributing the Exponent: The exponent -2 applies to everything inside the parentheses.
(5a³b⁴)⁻² = 5⁻² * (a³)⁻² * (b⁴)⁻²
-
Applying the Negative Exponent Rule: We apply the rule (x⁻ⁿ = 1/xⁿ) to each term.
5⁻² * (a³)⁻² * (b⁴)⁻² = 1/5² * 1/a⁶ * 1/b⁸
-
Simplifying: We calculate the numerical term and combine the fractions.
1/5² * 1/a⁶ * 1/b⁸ = 1/(25a⁶b⁸)
Final Answer
Therefore, the simplified form of (5a³b⁴)⁻² is 1/(25a⁶b⁸).
Key Points to Remember
- Negative exponents indicate reciprocals.
- Exponents distribute to all factors within parentheses.
- Simplify by applying the negative exponent rule and combining terms.