Simplify (3×6)¹⁰ ÷ (3×6)⁷: Division of Exponents Practice

We need to simplify the expression: $\frac{\left(3\times6\right)^{10}}{\left(3\times6\right)^7}$.

According to the Power of a Quotient Rule for Exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$, we can simplify any fraction where the numerator and the denominator have the same base and different exponents by subtracting their exponents.

In our case, the common base is $3\times6$. Let's apply the rule:

• The exponent in the numerator is 10.
• The exponent in the denominator is 7.

So, according to the rule, we subtract the exponent in the denominator from the exponent in the numerator:

$(3\times6)^{10-7}$.

Thus, the expression simplifies to $\left(3\times6\right)^{10-7}$.