A) x3•x5 •x b) x20: x : x14 c) (x8)3 : x16 d） x8:x5・（x2）2 e) (x6)3 : (x3)5

Let's simplify each of the given expressions step by step.

a) \( x^3 \cdot x^5 \cdot x \)

Using the property that \( x^a \cdot x^b = x^{a+b} \):

\[ x^3 \cdot x^5 \cdot x = x^{3+5+1} = x^{9} \]

b) \( \frac{x^{20}}{x \cdot x^{14}} \)

First, simplify the denominator:

\[ x \cdot x^{14} = x^{1+14} = x^{15} \]

Now, simplify the fraction:

\[ \frac{x^{20}}{x^{15}} = x^{20-15} = x^{5} \]

c) \( \frac{(x^8)^3}{x^{16}} \)

First, simplify the numerator using the power of a power property \( (x^a)^b = x^{a \cdot b} \):

\[ (x^8)^3 = x^{8 \cdot 3} = x^{24} \]

Now simplify the fraction:

\[ \frac{x^{24}}{x^{16}} = x^{24-16} = x^{8} \]

d) \( \frac{x^8}{x^5 \cdot (x^2)^2} \)

First, simplify \( (x^2)^2 \):

\[ (x^2)^2 = x^{2 \cdot 2} = x^{4} \]

Now simplify the denominator:

\[ x^5 \cdot x^4 = x^{5+4} = x^{9} \]

Now simplify the fraction:

\[ \frac{x^8}{x^{9}} = x^{8-9} = x^{-1} \]

e) \( \frac{(x^6)^3}{(x^3)^5} \)

Simplify the numerator and denominator using the power of a power property:

\[ (x^6)^3 = x^{6 \cdot 3} = x^{18} \]

\[ (x^3)^5 = x^{3 \cdot 5} = x^{15} \]

Now simplify the fraction:

\[ \frac{x^{18}}{x^{15}} = x^{18-15} = x^{3} \]

Summary of Results:

a) \( x^9 \)
b) \( x^5 \)
c) \( x^8 \)
d) \( x^{-1} \)
e) \( x^3 \)