Choose the expression that is equivalent to 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.
a 1 divided by 8 raised to the fourteenth power
b 814
c negative 1 divided by 8 raised to the fourteenth power
d −814
The expression is equivalent to:
$\frac{8^{-10}}{8^4 \cdot 8^0}$
Since $8^0 = 1$, we can simplify the denominator:
$\frac{8^{-10}}{8^4 \cdot 1}$
$= \frac{8^{-10}}{8^4}$
Next, we can subtract the exponents when dividing:
$= 8^{-10-4}$
$= 8^{-14}$
Therefore, the answer is choice $\boxed{\text{(a) 1 divided by 8 raised to the fourteenth power}}$.