Question

Which is the simplified form of (9c^-9)^-3?

Answer 1

b

Explanation:

Answer 2

We conclude that:

`\left(9c^(-9)\right)^(-3)=(c^(27))/(729)`

Explanation:

Given the expression

`\left(9c^(-9)\right)^(-3)`

Apply exponent rule:
`a^(-b)=(1)/(a^b)`

`\left(9c^(-9)\right)^(-3)=(1)/(\left(9c^(-9)\right)^3)`

Let us first solve:

`\left(9c^(-9)\right)^3`

Apply exponent rule:
`\left(a\cdot \:b\right)^n=a^nb^n`

`\left(9c^(-9)\right)^3=9^3\left(c^(-9)\right)^3`

`=729\left(c^(-9)\right)^3`

Apply exponent rule:
`\left(a^b\right)^c=a^(bc),\:\quad \mathrm{\:assuming\:}a\ge 0`

`=729c^(-9\cdot \:3)`

`=729c^(-27)`

Apply exponent rule:
`a^(-b)=(1)/(a^b)`

`=729\cdot (1)/(c^(27))`

`=(729)/(c^(27))`

Therefore, the expression
`\left(9c^(-9)\right)^(-3)=(1)/(\left(9c^(-9)\right)^3)` becomes

`\left(9c^(-9)\right)^(-3)=(1)/(\left(9c^(-9)\right)^3)`

`=(1)/((729)/(c^(27)))` ∵
`\left(9c^(-9)\right)^3=(729)/(c^(27))`

`=(c^(27))/(729)` ∵
`(1)/((b)/(c))=(c)/(b)`

Hence, we conclude that:

`\left(9c^(-9)\right)^(-3)=(c^(27))/(729)`