Which expressions are equivalent to ? Choose all the correct answers. Show your work.

Question 1

Question 2

Answer:

C, D, F

Explanation:

Exponent rules:

(a^b)/(a^c)=a^(b-c)

a^(-n)=(1)/(a^n)

(1)/(a^(-n))=a^n

$a^n \cdot b^n=(ab)^n$

a^0=1

(a^b)^c=a^(bc)

$\textsf{A}\quad(24^(-3))/(24^(-4))=24^(-3-(-4))=24^1=24$

$\textsf{B}\quad3^(-2) \cdot 8^(-5)=(1)/(3^2) \cdot (1)/(8^5)=(1)/(9) \cdot (1)/(32768)=(1)/(294912)$

$\textsf{C}\quad\left((1)/(24^(-7))\right)^(-1)=\left(24^7\right)^(-1)=24^(-7)$

$\textsf{D}\quad(8^(-7))/(3^7)=(1)/(8^7 \cdot 3^7)=(1)/((8 \cdot 3)^7)=(1)/(24^7)=24^(-7)$

$\textsf{E}\quad24^7 \cdot 24^0=24^7 \cdot 1=24^7$

$\textsf{F}\quad(24^3 \cdot 24^4)^(-1)=\left(24^(3+4)\right)^(-1)=(24^7)^(-1)=24^(-7)$

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