Final answer:
The expression (7³)² simplifies to 7⁶ because of the Exponent Rule, which states that when an exponent is raised to another exponent, you multiply them together.
Step-by-step explanation:
The manipulation of the expression (7³)² to 7⁶ is an application of the Exponent Rule. In general, when you have an exponent raised to another exponent, you multiply the exponents. This is represented by the formula (x⁺)⁻ = x¹⁺·⁻, where a and b are exponents.
Applying this rule, we transform (7³)² into 7¹(3××) which simplifies to 7⁶. This is a very useful property as it allows us to simplify expressions without having to expand them completely, which can save a lot of time and space, especially with larger exponents.