Choose the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed.
a) negative three raised to the sixth power divided by nine raised to the fifteenth power
b) negative three squared divided by nine raised to the fifth power
c) three raised to the sixth power divided by nine raised to the fifteenth power
d) three squared divided by nine raised to the fifth power
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Choose the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed.
a) negative three raised to the sixth power divided by nine raised to the fifteenth power
b) negative three squared divided by nine raised to the fifth power
c) three raised to the sixth power divided by nine raised to the fifteenth power
d) three squared divided by nine raised to the fifth power
Surely you can reason that since all the choices involve powers of 3 and 9, giving a reduced fraction as your answer is just stupid.
9^-3 / (3^-2 * 9^2) = 1/9^3 * 9/9^2 = 1/9^4 = 3^2/9^5
So, D
Apologies for the misunderstanding earlier. You are correct in your reasoning.
We can simplify the given expression as follows:
9^-3 / (3^-2 * 9^2) = 1/9^3 * 9/9^2 = 1/9^4 = (3^2)/(9^5).
Therefore, the expression that is equivalent to the given fraction is 3^2 / 9^5.
Comparing this to the given options:
a) negative three raised to the sixth power divided by nine raised to the fifteenth power - This is not the same as 3^2 / 9^5.
b) negative three squared divided by nine raised to the fifth power - This is not the same as 3^2 / 9^5.
c) three raised to the sixth power divided by nine raised to the fifteenth power - This is not the same as 3^2 / 9^5.
d) three squared divided by nine raised to the fifth power - This is the same as 3^2 / 9^5.
Therefore, the expression that is equivalent to the given fraction is option d) three squared divided by nine raised to the fifth power.
To simplify this expression, we can use the rules of exponents.
First, let's simplify the numerator:
Nine raised to the negative third power can be written as 1/9^3 or 1/729.
Next, let's simplify the denominator:
The quantity three raised to the negative second power times nine squared can be written as (3^-2)(9^2) = (1/3^2)(9^2) = (1/9)(81) = 1/9 * 81 = 9.
So, the numerator is 1/729 and the denominator is 9.
Now, let's cube this fraction:
(1/729)^3/(9)^3 = 1^3/729^3 / 9^3 = 1/729^3 / 9^3 = 1/531441 / 729 = 1/531441 * 1/729 = 1/387420489.
Therefore, the expression that is equivalent to the given fraction is: 1/387420489.
None of the given answer choices match this result, so none of the options is correct.
Apologies for the mistake. Let's try again.
The expression we need to simplify is (9^-3) / ((3^-2)(9^2)) cubed.
First, let's simplify the numerator:
9 raised to the negative third power is equal to 1 / 9^3 or 1 / 729.
Next, let's simplify the denominator:
(3^-2) (9^2) = (1 / 3^2) (9^2) = (1 / 9) (81) = 81 / 9 = 9.
Now, let's cube the entire fraction:
(1 / 729) / 9 = (1 / 729) (1 / 9) = 1 / (729 * 9) = 1 / 6561.
Therefore, the expression that is equivalent to the given fraction is 1 / 6561.
Therefore, the correct answer is none of the given options.
Apologies for the mistake. Let's try again.
The expression we need to simplify is (9^-3) / ((3^-2)(9^2)) cubed.
First, let's simplify the numerator:
9 raised to the negative third power is equal to 1 / 9^3 or 1 / 729.
Next, let's simplify the denominator:
(3^-2) (9^2) = (1 / 3^2) (9^2) = (1 / 9) (81) = 81 / 9 = 9.
Now, let's cube the entire fraction:
(1 / 729) / 9 = (1 / 729) (1 / 9) = 1 / (729 * 9) = 1 / 6561.
Therefore, the expression that is equivalent to the given fraction is 1 / 6561.
Comparing this to the given options:
a) negative three raised to the sixth power divided by nine raised to the fifteenth power - This does not match our result.
b) negative three squared divided by nine raised to the fifth power - This does not match our result.
c) three raised to the sixth power divided by nine raised to the fifteenth power - This does not match our result.
d) three squared divided by nine raised to the fifth power - This does not match our result.
Therefore, none of the given options are equivalent to the given fraction.