Choose the expression that is equivalent to fraction with 5 raised to the negative tenth power in the numerator and 5 raised to the fourth power times 5 raised to the zero power in the denominator.
a) negative 1 divided by 5 raised to the fourteenth power
b) −514
c) 1 divided by 5 raised to the fourteenth power
d) 514
The expression is equivalent to (5^-10) / (5^4 * 5^0)
Simplifying the expression within the denominator, we have 5^(4+0) = 5^4
So, the expression becomes (5^-10) / (5^4)
Using the rule of exponents that states when dividing the same base, you subtract the exponents, we get:
(5^-10) / (5^4) = 5^(-10-4) = 5^-14
Therefore, the expression is equivalent to 5 raised to the negative fourteenth power.
The correct answer is:
a) negative 1 divided by 5 raised to the fourteenth power