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