Simplify (17×3)^17 ÷ (17×3)^11: Laws of Exponents Practice

Let's start solving this equation step by step. The problem provided is:

$\frac{\left(17\times3\right)^{17}}{\left(17\times3\right)^{11}}=$

This problem involves the Power of a Quotient Rule for Exponents, which states:

• If you have a quotient of terms with the same base, you can subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.

The terms in our problem already have the same base $(17\times3)$. Therefore, we apply the rule directly:

$\frac{\left(17\times3\right)^{17}}{\left(17\times3\right)^{11}} = \left( 17 \times 3 \right)^{17-11}$

Simplifying the exponent gives

$17 - 11 = 6$

Thus, the expression simplifies to:

$\left(17 \times 3\right)^6$

Therefore, the solution to the question is:

$\left(17 \times 3\right)^6$