Question

Simplify (9−9)−2\left(9^{-9}\right)^{-2}(9

−9
)
−2
. Write your answer in exponential form. (Example: 525^25
2
not 252525

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression, we can start by evaluating the exponent 9^{-9}.

As the exponent is negative, we can rewrite it as 1/(9^9):

9^{-9} = 1/(9^9)

Now, we can substitute this value back into the expression:

(9−9)−2(9^{-9})^{-2}(9−9)
= 0 - 2(1/(9^9))^{-2}(0)
= -2(1/(9^9))^{-2}(0)
= -2(1/((9^9)^2))(0)
= -2(1/(9^18))(0)
= 0

Therefore, the simplified expression is 0.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression (9−9)−2\left(9^{-9}\right)^{-2}(9

−9
)
−2
, we start by evaluating the innermost parentheses first.

Inside the parentheses, 9 - 9 equals 0:

(0)−2\left(9^{-9}\right)^{-2}(9
0
)
−2


Next, we can simplify the expression 9^-9:

(0)−2\left(\frac{1}{9^9}\right)^{-2}(9
0
)
−2


Using the property of exponents, we can rewrite 1/9^9 as (9^9)^-1:

(0)−2\left((9^9)^{-1}\right)^{-2}(9
0
)
−2


Now, we can simplify the exponent inside the parentheses by applying the power of a power rule, where we multiply the exponents:

(0)−2(9^{9 \cdot -1})^{-2}(9
0
)
−2


Simplifying the exponent 9 * -1 gives us -9:

(0)−2(9^{-9})^{-2}(9
0
)
−2


Now, let's apply the power of a power rule again by multiplying the exponents:

(0)−2(9^{-9 \cdot -2})(9
0
)
−2


Simplifying the exponent -9 * -2 gives us 18:

(0)−2(9^{18})(9
0
)
−2


We know that any number raised to the power of 0 equals 1. Therefore, (0)^-2 can be rewritten as 1:

1 \cdot (9^{18})(9
1
)
−2


Finally, using the product of powers rule, we multiply the exponents:

9^{18+1} \cdot (9
9
)^{-2}


Simplifying the exponent 18 + 1 gives us 19:

9^{19} \cdot (9
9
)^{-2}


Therefore, after simplifying, the expression (9−9)−2\left(9^{-9}\right)^{-2}(9
−9
)
−2
can be written as 9^19 \cdot (9
9
)^{-2}.