Final answer:
To evaluate the expression with the given variables, substitute −35 for a and −6.75 for b. The numerator simplifies to −83. The denominator, (−6.75)^{15}, will be a very small negative number due to the large exponent, resulting in a large negative value for the entire fraction. The exact value would require the use of a calculator.
Step-by-step explanation:
To evaluate the expression (2a−13)/b^{15} with the given values a = −35 and b = −6.75, first substitute the given values into the expression:
(2(−35)−13)/(−6.75)^{15}.
Calculating the numerator gives us:
2(−35) = −70, and −70−13 = −83.
Now the expression is:
−83/(−6.75)^{15}
The value of the denominator is a very small number, as any non-zero number raised to the power of 15 will be substantial, and a negative base results in a negative result. Therefore, b^{15} with a negative base will be a negative number, and the exponent will make the number very small.
Because the denominator is such a small negative number, the fraction itself will result in a large negative number. Exact calculation would require a calculator due to the large exponent on the denominator.