Simplify. Express your answer using exponents. (5q^6r^5s^7)^3 Submit

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}).