Answered

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24. Simplify the expression.

[tex]\[ \frac{x^5}{x^9} \][/tex]

A. \( x^4 \)
B. \( \frac{1}{x^{14}} \)
C. \( x^{14} \)
D. [tex]\( \frac{1}{x^4} \)[/tex]

Sagot :

GinnyAnswer
To simplify the expression
[tex]\[ \frac{x^5}{x^9} \][/tex]

we can use the properties of exponents. Specifically, when we divide like bases, we subtract the exponents:
[tex]\[ \frac{x^a}{x^b} = x^{a-b} \][/tex]

Here, \( a = 5 \) and \( b = 9 \), so we subtract the exponent in the denominator from the exponent in the numerator:

[tex]\[ \frac{x^5}{x^9} = x^{5-9} \][/tex]

Simplifying the exponent:
[tex]\[ 5 - 9 = -4 \][/tex]

So the expression becomes:
[tex]\[ x^{-4} \][/tex]

This can also be written as:

[tex]\[ \frac{1}{x^4} \][/tex]

Thus, the simplified form of the expression \( \frac{x^5}{x^9} \) is:
[tex]\[ \frac{1}{x^4} \][/tex]

Among the given choices, the correct answer is:

[tex]\[ \boxed{\frac{1}{x^4}} \][/tex]
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