Question

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

Answer 1

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)`