To evaluate the expression \( a^5 - bc + \frac{4a}{c} \) with 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 \( bc \): \[ bc = 3 \times 8 = 24 \]
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Calculate \( \frac{4a}{c} \): \[ \frac{4a}{c} = \frac{4 \times 2}{8} = \frac{8}{8} = 1 \]
Now, substitute these values back into the expression: \[ 32 - 24 + 1 \]
- Now perform the arithmetic: \[ 32 - 24 = 8 \] \[ 8 + 1 = 9 \]
Therefore, the value of the expression \( a^5 - bc + \frac{4a}{c} \) when \( a = 2 \), \( b = 3 \), and \( c = 8 \) is \( \boxed{9} \).
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