Simplify (5a)^10 ÷ (5a)^2: Power Division with Compound Base

To solve the given expression $\frac{\left(5\times a\right)^{10}}{\left(5\times a\right)^2}$, we apply the Power of a Quotient Rule for exponents. This rule states that $\frac{b^m}{b^n} = b^{m-n}$, where 'b' is a base and 'm' and 'n' are exponents.

In the given expression, the base is $5 \times a$, and the exponents are 10 and 2, respectively.

Following the rule, we subtract the exponent in the denominator from the exponent in the numerator:

• Numerator exponent: 10
• Denominator exponent: 2
• Subtract the exponents: $10 - 2 = 8$

Thus, we rewrite the expression as
$\left(5\times a\right)^8$

The solution to the question is: $\left(5\times a\right)^8$.