Question

Which expression is equivalent to (9 ^ - 2 * 3 ^ 5) ^ - 2

- (3 ^ 3)/(9 ^ 4)

(3 ^ 3)/(9 ^ 4)

- (9 ^ 4)/(3 ^ 10)

(9 ^ 4)/(3 ^ 10)

Answer 1

To find the equivalent expression for (9^(-2) * 3^5)^(-2), you can use the properties of exponents.

First, let's simplify the inner expression:

(9^(-2) * 3^5) = (1/9^2 * 3^5) = (1/81 * 243) = 3^5 / 81

Now, raise this result to the power of -2:

(3^5 / 81)^(-2)

To simplify this further, you can apply the negative exponent by reciprocating the fraction and changing the exponent's sign:

(81 / 3^5)^2

Now, simplify the fraction inside:

(81 / 243)^2 = (1/3)^2

So, the equivalent expression is (1/3)^2, which is the same as 1/9.

Therefore, the correct option is: (3^3)/(9^4).