Question

((-6/11)^-5)^-3 simplify​

Answer 1

Answer:

$\displaystyle\mathrm{Simplify}\:\left(\left(-\frac{6}{11}\right)^{-5}\right)^{-3}:\quad -\frac{6^{15}}{11^{15}}\quad \left(\mathrm{Decimal:\quad }\:-0.00011\dots \right)$

Step-by-step explanation:

$\left(\left(-\dfrac{6}{11}\right)^{-5}\right)^{-3}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}}$

$=\left(-\dfrac{6}{11}\right)^{\left(-5\right)\left(-3\right)}$

$\gray{\left(-5\right)\left(-3\right)=15}$

$=\left(-\dfrac{6}{11}\right)^{15}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\mathrm{if\:}n\mathrm{\:is\:odd}}$

$\displaystyle\gray{\left(-\frac{6}{11}\right)^{15}=-\left(\frac{6}{11}\right)^{15}}$

$=-\left(\dfrac{6}{11}\right)^{15}$

$\displaystyle\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}}$

$\displaystyle\gray{\left(\frac{6}{11}\right)^{15}=\frac{6^{15}}{11^{15}}}$

$=-\dfrac{6^{15}}{11^{15}}$