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Math Trailhead

Worksheet Exponent Rules

14.

(a) Simplify \(\displaystyle{\frac{c^{6}}{c^{9}}}\) and write your answer without using negative exponents.
(b) Simplify \(\displaystyle{\frac{c^{6}}{c^{-9}}}\) and write your answer without using negative exponents.
(c) Simplify \(\displaystyle{\frac{c^{-6}}{c^{9}}}\) and write your answer without using negative exponents.
(d) Simplify \(\displaystyle{\frac{c^{-6}}{c^{-9}}}\) 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.
\(\frac{1}{c^{3}}\)
Answer 2.
Answer 3.
\(\frac{1}{c^{15}}\)
Answer 4.
Solution.
Part (a):
\(\frac{c^{6} }{ c^{9}} = c^{(6-9)} = c^{-3} = \frac{1}{c^{3}}\)
Part (b):
\(\frac{c^{6} }{ c^{-9}} = c^{(6-(-9))} = c^{15}\)
Part (c):
\(\frac{c^{-6} }{ c^{9}} = c^{(-6-9)} = c^{-15} = \frac{1}{c^{15}}\)
Part (d):
\(\frac{c^{-6} }{ c^{-9}} = c^{(-6-(-9))} = c^{3}\)