Choose the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power end quantity all raised to the negative third power.
a −76
b 1 divided by 7 raised to the third power
c negative 1 divided by 7 raised to the sixth power
d 718
The expression 7 raised to the negative second power is equivalent to 1 divided by 7 squared (1/7^2).
The expression 7 raised to the third power is 7 cubed (7^3).
When we multiply these two expressions and then raise the result to the negative third power, we get (1/7^2 * 7^3)^-3.
Using the rule of exponents for multiplying and raising to a power, we can simplify this expression as (7^-6)^-3.
When we raise a number to a negative power, it is the same as taking the reciprocal of the number raised to the positive power. So, (7^-6)^-3 = 1/(7^6)^-3.
Using the rule of exponents for raising to a power, we can simplify further to 1/7^-18.
Finally, using the rule of exponents for negative exponents, we can rewrite this expression as 7^18.
Therefore, the expression is equivalent to 7^18, and the correct answer is d) 718.