To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\displaystyle \left (- \frac{3}{2} \right )^{5} = - \left ( \frac{3}{2}\right )^{5} = - \left ( \frac{3^{5}} {2^{5}} \right ) = - \left ( \frac{3 \times 3 \times 3\times 3 \times 3 }{2\times 2 \times 2 \times 2 \times 2 } \right ) = -\frac{243}{32}$

To solve for $\displaystyle x$, we need to cross multiply.

$\displaystyle \frac{2}{3x}=\frac{9}{5}$

$\displaystyle 2\times5=9\times3x$

$\displaystyle 10=27x$

Divide both sides by 27 to isolate the variable.

$\displaystyle \frac{10}{27}=x$

The fraction cannot be reduced, making this our final answer.

The expression, $\displaystyle \frac{63}{9}\cdot\frac{3}{2}$ is equal to:

$\displaystyle (63\div9)\cdot\frac{3}{2}$

This is equal to:

$\displaystyle 7\cdot \frac{3}{2}$

This equals:

$\displaystyle \frac{21}{2}=10\frac{1}{2}$

To multiply fractions, simply multiply the first numerator by the second numerator and the first denominator by the second denominator.  Simply when necessary. 

$\displaystyle 2\times5=10$

$\displaystyle 7\times9=63$

$\displaystyle \frac{2}{7}\times \frac{5}{9}=\frac{10}{63}$

To find the answer, you must multiple the fractions together.  

When multiplying fractions, all you have to do is multiple the numerators together and the denominators together.  

So 

$\displaystyle 1*7=7$ 

and 

$\displaystyle 5*6=30$ 

giving us 

$\displaystyle \frac{7}{30}$.

To multiply fractions, you must multiple the numerators and denominators.  

So 

$\displaystyle 6*1=6$ 

and 

$\displaystyle 9*7=63$.  

Your final answer is $\displaystyle \frac{6}{63}=\frac{3\cdot 2}{3\cdot 21}=\frac{2}{21}$.

To multiply fractions, you multiply the numerators

$\displaystyle 5*3=15$ 

and multiply the denominators

$\displaystyle 6*4=24$ 

to get,

 $\displaystyle \frac{15}{24}$.  

They each have a common factor of $\displaystyle 3$ so it reduces down to $\displaystyle \frac{5}{8}$ by dividing each.

When multiplying fractions, we will first multiply the numerators, then we will multiply the denominators.

So, given the fractions

$\displaystyle \frac{2}{3} \cdot \frac{1}{3}$

when multiplying, we will get

$\displaystyle \frac{2}{3} \cdot \frac{1}{3} = \frac{2 \cdot 1}{3 \cdot 3}$

$\displaystyle \frac{2}{3} \cdot \frac{1}{3} = \frac{2}{9}$

Simplify the following expression:

$\displaystyle \frac{4}{5}*\frac{8}{9}$

To multiply fractions, simply multiply across the top and bottom:

$\displaystyle \frac{4}{5}*\frac{8}{9}=\frac{4*8}{5*9}=\frac{32}{45}$

Now, we cannot simplify our answer, so our answer remains:

$\displaystyle \frac{32}{45}$

When we multiply fractions, we first multiply the numerators, then we multiply the denominators.  We do not need to find common denominators when multiplying.  So in

$\displaystyle \frac{2}{3} \cdot \frac{4}{5}$

we will multiply.  We get

$\displaystyle \frac{2 \cdot 4}{3 \cdot 5}$

$\displaystyle \frac{8}{15}$