To simplify the expression \(\left(\dfrac{3^{-6}}{7^{-3}}\right)^{5}\), we will follow these steps:
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Simplify the inner fraction: \[ \dfrac{3^{-6}}{7^{-3}} = 3^{-6} \cdot 7^{3} = \dfrac{7^{3}}{3^{6}}. \]
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Now raise the fraction to the power of 5: \[ \left(\dfrac{7^{3}}{3^{6}}\right)^{5} = \dfrac{(7^{3})^{5}}{(3^{6})^{5}}. \]
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Apply the power rule \((a^{m})^{n} = a^{m \cdot n}\): \[ (7^{3})^{5} = 7^{15} \quad \text{and} \quad (3^{6})^{5} = 3^{30}. \]
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Therefore, the expression becomes: \[ \dfrac{7^{15}}{3^{30}}. \]
Now, let's compare this expression with the given choices:
- (Choice A): \(\dfrac{7^{15}}{3^{30}}\)
- (Choice B): \(\dfrac{7^{3}}{3^{-30}}\)
- (Choice C): \(\dfrac{3^{15}}{7^{30}}\)
Since we have determined that the simplified expression is \(\dfrac{7^{15}}{3^{30}}\), the equivalent expression is:
Choice A: \(\dfrac{7^{15}}{3^{30}}\).