Choose the expression that is equivalent to the quantity 9 raised to the negative second power times 9 raised to the seventh power end quantity all raised to the negative third power
a) −99
b) negative 1 divided by 9 raised to the sixth power
c) 1 divided by 9 raised to the fifteenth power
d) 927
To simplify this expression, we need to remember the rule for multiplying exponents with the same base: when you multiply two exponents with the same base, you add the exponents.
First, we simplify the expression inside the parentheses.
9 raised to the negative second power times 9 raised to the seventh power is equal to 9 raised to the negative second power plus seventh power.
9^(-2) * 9^7 = 9^(7 - 2) = 9^5.
Next, we raise this result to the negative third power.
(9^5)^(-3) = 9^(5 * -3) = 9^(-15).
Hence, the equivalent expression is 1 divided by 9 raised to the fifteenth power, which is option c) 1 divided by 9 raised to the fifteenth power.