%5E2.jpeg "(-8a^5)^2")
Simplifying (-8a^5)^2
In mathematics, simplifying expressions is a fundamental skill. One common type of simplification involves exponents, particularly when dealing with expressions raised to a power. Let's take a look at how to simplify the expression (-8a^5)^2.
Understanding the Rules
Before we dive into the simplification, let's recall some key rules about exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Rules
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Apply the power of a product rule: (-8a^5)^2 = (-8)^2 * (a^5)^2
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Apply the power of a power rule: (-8)^2 * (a^5)^2 = 64 * a^(5*2)
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Simplify the exponent: 64 * a^(5*2) = 64 * a^10
Final Result
Therefore, the simplified expression of (-8a^5)^2 is 64a^10.
Key Points to Remember
- Remember to apply the power to both the coefficient and the variable.
- Be mindful of negative signs within parentheses. When squaring a negative number, the result is always positive.
- Practice these rules to become comfortable with simplifying expressions involving exponents.