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Math Trailhead

Worksheet Exponent Rules

14.

(a) Simplify \(\displaystyle{\frac{x^{9}}{x^{14}}}\) and write your answer without using negative exponents.
(b) Simplify \(\displaystyle{\frac{x^{9}}{x^{-14}}}\) and write your answer without using negative exponents.
(c) Simplify \(\displaystyle{\frac{x^{-9}}{x^{14}}}\) and write your answer without using negative exponents.
(d) Simplify \(\displaystyle{\frac{x^{-9}}{x^{-14}}}\) and write your answer without using negative exponents.
Hint.
Recall the exponent property: \(\displaystyle \frac{B^m}{B^n} = B^{(m-n)}\)
Also remember that results with negative exponents may be rewritten as \(B^{(-p)} = \frac{1}{B^p}\)
Answer 1.
\(\frac{1}{x^{5}}\)
Answer 2.
Answer 3.
\(\frac{1}{x^{23}}\)
Answer 4.
Solution.
Part (a):
\(\frac{x^{9} }{ x^{14}} = x^{(9-14)} = x^{-5} = \frac{1}{x^{5}}\)
Part (b):
\(\frac{x^{9} }{ x^{-14}} = x^{(9-(-14))} = x^{23}\)
Part (c):
\(\frac{x^{-9} }{ x^{14}} = x^{(-9-14)} = x^{-23} = \frac{1}{x^{23}}\)
Part (d):
\(\frac{x^{-9} }{ x^{-14}} = x^{(-9-(-14))} = x^{5}\)