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

Question

asked Dec 28, 2022 111k views

2 Answers

Aarbor · Answer 1 · 2023-01-01T02:38:09+0000

Answer:

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:

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