%5E2(x%5E8)%5E1%2F2.jpeg "(7x^3)^2(x^8)^1/2")
Simplifying Expressions with Exponents
This article will guide you through the process of simplifying the expression (7x³)²(x⁸)¹/².
Understanding the Rules
To simplify this expression, we'll need to utilize the following rules of exponents:
- Product of Powers: When multiplying powers with the same base, add the exponents. (xᵃ * xᵇ = xᵃ⁺ᵇ)
- Power of a Power: When raising a power to another power, multiply the exponents. ( (xᵃ)ᵇ = xᵃᵇ)
- Fractional Exponent: A fractional exponent indicates a root. (x¹/ⁿ = ⁿ√x)
Step-by-Step Simplification
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Simplify the first term: (7x³)² = 7² * (x³)², applying the power of a power rule. This simplifies to 49x⁶.
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Simplify the second term: (x⁸)¹/² = x⁸ * ¹/², applying the power of a power rule. This simplifies to x⁴.
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Combine the simplified terms: 49x⁶ * x⁴ = 49x¹⁰, applying the product of powers rule.
Final Result
Therefore, the simplified form of the expression (7x³)²(x⁸)¹/² is 49x¹⁰.