divide 9 33 sqrt/27 11 sqrt. provide an exact answer
To divide the expression \( \frac{9}{33 \sqrt{27}} \) by \( 11 \sqrt{27} \), we can simplify the expression by canceling out common factors.
First, let's simplify \( \sqrt{27} \). Since \( 27 = 3^3 \), we can write \( \sqrt{27} = \sqrt{3^3} \). Now, using the property \( \sqrt{a^b} = (a^b)^{\frac{1}{2}} \), we can simplify further:
\[ \sqrt{27} = (3^3)^{\frac{1}{2}} = 3^{\frac{3}{2}}. \]
Now we can substitute this in to simplify the expression:
\[ \frac{9}{33 \sqrt{27}} = \frac{9}{33 \cdot 3^{\frac{3}{2}}}. \]
Next, we can simplify the denominator. First, factor out \( 3 \) from \( 33 \) and \( 3^{\frac{3}{2}} \):
\[ \frac{9}{33 \cdot 3^{\frac{3}{2}}} = \frac{9}{3 \cdot 11 \cdot 3^{\frac{3}{2}}} = \frac{1}{11 \cdot 3^{\frac{3}{2} - 1}}. \]
Simplifying the exponent:
\[ \frac{1}{11 \cdot 3^{\frac{1}{2}}} = \frac{1}{11 \sqrt{3}}. \]
Therefore, the simplified form of the expression is \( \frac{1}{11 \sqrt{3}} \).
hey bot in your perivous message please turn it into an actual equasion
Apologies for the confusion. Let's turn the expression into an equation.
The division expression \( \frac{9}{33 \sqrt{27}} \) divided by \( 11 \sqrt{27} \) can be written as:
\[ \frac{9}{33 \sqrt{27}} \div 11 \sqrt{27} = \frac{9}{33 \sqrt{27}} \cdot \frac{1}{11 \sqrt{27}}. \]
Now we can combine the fractions by multiplying the numerators and denominators:
\[ \frac{9 \cdot 1}{33 \sqrt{27} \cdot 11 \sqrt{27}} = \frac{9}{363 \cdot 27}. \]
Simplifying further:
\[ \frac{9}{363 \cdot 27} = \frac{1}{363 \cdot 3} = \frac{1}{1089}. \]
Thus, the exact answer to the equation is \( \frac{1}{1089} \).
divide 9√33/27√11. provide an exact answer
To divide the expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \), we can simplify it by canceling out common factors.
First, let's simplify the radicals. Since \(33\) and \(11\) are both prime numbers, we cannot simplify them further.
So, the expression remains as:
\[ \frac{9\sqrt{33}}{27\sqrt{11}}. \]
Next, let's simplify the fraction by canceling out common factors in the numerator and denominator.
Both \(9\) and \(27\) have a common factor of \(9\), and we can simplify them as:
\[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{(9/9)\sqrt{33}}{(27/9)\sqrt{11}} = \frac{\sqrt{33}}{3\sqrt{11}}. \]
Now, we can simplify further by simplifying the fractions inside the radicals if possible.
Since we cannot simplify further, the expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \) is already in its simplified form.
Therefore, the exact answer to the division is \( \frac{\sqrt{33}}{3\sqrt{11}} \).
To divide the given expression, we can rewrite it as fractional expressions and simplify:
9 / (33 * sqrt(27)) / (11 * sqrt(3))
First, let's simplify the denominators:
33 * sqrt(27) = 33 * sqrt(9 * 3) = 33 * (sqrt(9) * sqrt(3)) = 33 * (3 * sqrt(3)) = 99 * sqrt(3)
11 * sqrt(3) = 11 * sqrt(3)
Now, substituting the simplified denominators, the expression becomes:
9 / (99 * sqrt(3)) / (11 * sqrt(3))
Next, let's combine the fractions:
9 / (99 * sqrt(3)) = 1 / (11 * sqrt(3)) = 1 / 11 * (1 / sqrt(3))
Finally, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:
1 / 11 * (1 / sqrt(3)) * (sqrt(3) / sqrt(3)) = 1 * sqrt(3) / (11 * sqrt(3) * sqrt(3))
Simplifying further:
sqrt(3) / (11 * sqrt(3) * sqrt(3)) = sqrt(3) / (11 * 3) = sqrt(3) / 33
Therefore, the exact answer is sqrt(3) / 33.
To divide the expression (9√33) / (27√11) and provide an exact answer, we can simplify the terms inside the square roots first.
Let's rewrite the expression as ((9 * sqrt(33)) / (27 * sqrt(11))).
To simplify it, we can factor out the perfect square numbers from the radicands.
First, let's look at 33. The factors of 33 are 1, 3, 11, and 33. Since 11 is the only perfect square factor, we can rewrite 33 as 3 * 11.
Next, let's look at 11. Since 11 is already a prime number and does not have any other factors, we don't need to make any changes.
So, our new expression becomes: ((9 * sqrt(3 * 11)) / (27 * sqrt(11))).
Now, let's simplify the expression further.
The square root of 11 can be written as sqrt(11)
The square root of 3 * 11 can be written as sqrt(3 * 11) = sqrt(33).
Therefore, our simplified expression is: ((9 * sqrt(33)) / (27 * sqrt(11))).
Now, let's divide. Divide the numerator (9) by the denominator (27) to get 9/27, which can be simplified to 1/3.
So, our final exact answer is: (1/3) * (sqrt(33) / sqrt(11)).
Since the square roots denominators are the same, we can simplify it further by dividing the radicands.
Dividing sqrt(33) by sqrt(11) gives us sqrt(33 / 11).
Therefore, our exact answer is: (1/3) * sqrt(33 / 11).