Question

Which expressions are equivalent to StartFraction 1 Over 36 EndFraction? Check all that apply. 3 Superscript negative 6 6 Superscript negative 2 StartFraction 6 cubed Over 6 Superscript 5 EndFraction StartFraction 6 squared Over 6 Superscript negative 1 EndFraction 6 times 6 Superscript negative 2 6 Superscript negative 9 Baseline times 6 Superscript 7

Answer 1

Answer:

(6^3)/(6^5)

6^- 2

(6^- 9) * (6^7)

Step-by-step explanation:

3^(- 6)

= 1/3^6        (since we know that a^(- 1) = 1/a^1 = 1/a)

= 1/729

6^(- 2)

= 1/(6^2)     (since we know that a^(- 1) = 1/a^1 = 1/a)

= 1/36

6^3/6^5

= 6^(3 - 5)     (since we know if the bases are the same then powers can be manipulated like regular math problems)  

= 6^(- 2)      (since we know that a^(- 1) = 1/a^1 = 1/a)

= 1/6^2

= 1/36

6^2 / 6^(- 1)

= 6^(2 - (- 1))   (since we know if the bases are the same then powers can be manipulated like regular math problems)  

= 6^(2 + 1)

= 6^3

= 216

6*6^-2

= (6^1) * (6^- 2)

= 6^(1 - 2)

= 6^(- 1)

= 1/(6^1)    (since we know that a^(- 1) = 1/a^1 = 1/a)

= 1/6

6^(- 9) * 6^7

= 6^(- 9 + 7)  (since we know if the bases are the same then powers can be manipulated like regular math problems)  

= 6^ (- 2)     (since we know that a^(- 1) = 1/a^1 = 1/a)

= 1/6^2

= 1/36

Hope this helps, and please mark me brainliest if it does!

Answer 2

Answer:

6^-2

6^3/6^5

6^-9 *6^ 7

Step-by-step explanation:

We want the fractions equal to 1/36

We know that a^-b = 1/a^b

We also know that a^b / a^c = a^(b-c)

We also know that a^b * a^c = a^(b+c)

3^ -6 = 1/3^6 = 1/729

6^-2 = 1/6^2 = 1/36

6^3/6^5 = 6^(3-5) = 6^-2 = 1/6^2 = 1/36

6^2 / 6^-1 = 6^(2- -1) = 6^3 = 216

6*6^-2 = 6^(1-2) = 6^-1 = 1/6

6^-9 *6^ 7 = 6^(-9+7) = 6^ -2 = 1/6^2 = 1/36