Simplify. Express your answer using exponents. (11p^6q^6r^5)^2

To simplify the expression ((11p^6q^6r^5)^2), you will need to apply the power of a product rule, which states that ((ab)^n = a^n b^n), and the power of a power rule, which means ((x^m)^n = x^{mn}).

Here’s how to do it step by step:

1. Apply the exponent to the coefficient and each variable:

[

(11)^2 cdot (p^6)^2 cdot (q^6)^2 cdot (r^5)^2

]

2. Calculate each part:

– (11^2 = 121)

– ((p^6)^2 = p^{6 cdot 2} = p^{12})

– ((q^6)^2 = q^{6 cdot 2} = q^{12})

– ((r^5)^2 = r^{5 cdot 2} = r^{10})

3. Combine them together:

[

121p^{12}q^{12}r^{10}

]

So, the simplified expression, using exponents, is:

[

boxed{121p^{12}q^{12}r^{10}}

]