To evaluate the expression \( a^5 - bc + \frac{4a}{c} \) using the values \( a = 2 \), \( b = 3 \), and \( c = 8 \), we can substitute these values into the expression step by step.
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Calculate \( a^5 \): \[ a^5 = 2^5 = 32 \]
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Calculate \( bc \): \[ bc = 3 \cdot 8 = 24 \]
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Calculate \( \frac{4a}{c} \): \[ \frac{4a}{c} = \frac{4 \cdot 2}{8} = \frac{8}{8} = 1 \]
Now substitute these results back into the expression: \[ a^5 - bc + \frac{4a}{c} = 32 - 24 + 1 \]
Now simplify: \[ 32 - 24 = 8 \] \[ 8 + 1 = 9 \]
Thus, the value of the expression is: \[ \boxed{9} \]
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