Final answer:
The equivalent expression is 1 divided by 8 raised to the fourteenth power, which is obtained by applying exponent rules such as subtracting exponents when dividing like bases and expressing negative exponents as reciprocals.
Therefore, the correct answer is: option "1 divided by 8 raised to the fourteenth power."
Step-by-step explanation:
The expression that is equivalent to a fraction with 8 raised to the negative tenth power in the numerator and 8 raised to the fourth power times 8 raised to the zero power in the denominator can be simplified using exponent rules.
Remember that a nonzero number raised to the zero power is 1, so 80 is 1, and it does not affect the calculation.
Then, utilize the property that states to divide powers with the same base, subtract the exponents.
Here, the expression simplifies as follows:
8-10 / (84 × 80)
= 8-10 / 84
= 8-10 - 4
= 8-14.
To express a negative exponent as a positive exponent in the denominator, recall that x-n = 1 / xn.
Thus, 8-14 equals 1 divided by 8 raised to the fourteenth power.