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)
StepbyStep Simplification

Simplify the first term: (7x³)² = 7² * (x³)², applying the power of a power rule. This simplifies to 49x⁶.

Simplify the second term: (x⁸)¹/² = x⁸ * ¹/², applying the power of a power rule. This simplifies to x⁴.

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.