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 \( \frac{1}{11 \sqrt{3}} \).
divide 9 33 sqrt/27 11 sqrt. provide an exact answer
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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 \( \frac{1}{1089} \).
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 \( \frac{\sqrt{33}}{3\sqrt{11}} \).
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 \( \frac{\sqrt{33}}{3\sqrt{11}} \).
1 answer