Simplify. Express your answer using exponents.
(5q^6r^5s^7)^3
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Simplify. Express your answer using exponents. (5q^6r^5s^7)^3 Submit
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To simplify the expression ((5q^6r^5s^7)^3) and express it using exponents, we apply the power of a power property. This property states that ((a^m)^n = a^{m cdot n}).
Here’s how to simplify it step by step:
1. Apply the exponent to each factor inside the parentheses:
– For the coefficient: (5^3 = 125)
– For (q^6): ((q^6)^3 = q^{6 cdot 3} = q^{18})
– For (r^5): ((r^5)^3 = r^{5 cdot 3} = r^{15})
– For (s^7): ((s^7)^3 = s^{7 cdot 3} = s^{21})
2. Combine the results:
Therefore, when we combine everything, we get:
[
(5q^6r^5s^7)^3 = 125q^{18}r^{15}s^{21}
]
So, the simplified expression is (125q^{18}r^{15}s^{21}).