Let's solve the expression step by step:
The given expression is
\[ 15 \times 8^{\frac{8}{5}} + 4 \times (7^0 - 6) \]
First, calculate \(7^0\):
\[ 7^0 = 1 \]
Now substitute this back into the expression:
\[ 15 \times 8^{\frac{8}{5}} + 4 \times (1 - 6) \]
Next, calculate \(1 - 6\):
\[ 1 - 6 = -5 \]
Substituting this back into the expression, we get:
\[ 15 \times 8^{\frac{8}{5}} + 4 \times (-5) \]
Calculating \(4 \times (-5)\):
\[ 4 \times (-5) = -20 \]
Now the expression is:
\[ 15 \times 8^{\frac{8}{5}} - 20 \]
Next, calculate \(8^{\frac{8}{5}}\):
First, we rewrite 8 as \(2^3\):
\[ 8^{\frac{8}{5}} = (2^3)^{\frac{8}{5}} = 2^{\frac{24}{5}} \]
Now we'll calculate \(15 \times 8^{\frac{8}{5}} = 15 \times 2^{\frac{24}{5}}\).
Instead of calculating \(2^{\frac{24}{5}}\) exactly, we can express it alone, but if you wanted a decimal approximation, it would need a calculator.
For now, let's calculate \(15 \times 8^{\frac{8}{5}}\) in terms of \(2^{\frac{24}{5}}\):
\[ = 15 \times 2^{\frac{24}{5}} - 20 \]
Since this can't be simplified further without a calculator for the exact numerical value of \(2^{\frac{24}{5}}\), we can conclude our expression as:
\[ 15 \times 2^{\frac{24}{5}} - 20 \]
If you need the decimal approximation for precision, then \(2^{\frac{24}{5}} \approx 54.736\) leading to:
\[ 15 \times 54.736 - 20 \approx 821.04 - 20 = 801.04 \]
Thus, the final approximate answer is:
\[ 801.04 \]