Question

40 pts- please help <3
How can the following expression be
written so that no negative exponents
appear?

Answer 1

Answer:

$c^2$

Step-by-step explanation:

Given expression:

$\left(\dfrac{c^{-3}c^4}{c^2}\right)^{-2}$

$\textsf{Apply the product rule of exponents} \quad a^b \cdot a^c=a^{b+c}:$

$\implies \left(\dfrac{c^{-3+4}}{c^2}\right)^{-2}$

$\implies \left(\dfrac{c^{1}}{c^2}\right)^{-2}$

$\textsf{Apply the quotient rule of exponents} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies \left(c^{1-2}\right)^{-2}$

$\implies \left(c^{-1}\right)^{-2}$

$\textsf{Apply the power of a power rule of exponents} \quad (a^b)^c=a^{bc}:$

$\implies c^{(-1 \cdot-2)}$

$\implies c^2$

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