To solve the expression \( 15 \times 8^{\frac{8}{5}} + 4 \times (7^{0} - 6) \), let's break it down step by step.
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Calculate \( 8^{\frac{8}{5}} \):
- Using a calculator or simplifying the expression, we find: \[ 8 = 2^3 \quad \text{so} \quad 8^{\frac{8}{5}} = (2^3)^{\frac{8}{5}} = 2^{\frac{24}{5}} = 2^{4.8} \]
- To get an approximate value, \( 2^{4.8} \approx 27.6309 \).
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Calculate \( 15 \times 8^{\frac{8}{5}} \): \[ 15 \times 27.6309 \approx 414.4635 \]
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Calculate \( 7^{0} \):
- Any non-zero number raised to the power of 0 is 1: \[ 7^{0} = 1 \]
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Substitute \( 7^{0} \) back into the expression:
- Now we calculate \( 4 \times (1 - 6) \): \[ 1 - 6 = -5 \] \[ 4 \times (-5) = -20 \]
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Combine both parts: \[ 15 \times 8^{\frac{8}{5}} + 4 \times (7^{0} - 6) \approx 414.4635 - 20 = 394.4635 \]
Thus, the final answer is approximately: \[ \boxed{394.4635} \]