Question

Please help me with this problem Evaluate (-½·3)³

Answer 1

Answer: -27/8

Step-by-step explanation:

$\left(-\frac{1}{2}\cdot \:3\right)^3$

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

$\left(-\frac{1}{2}\cdot \:3\right)^3=-\left(\frac{1}{2}\cdot \:3\right)^3$

$=-\left(\frac{1}{2}\cdot \:3\right)^3$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n$

$\left(\frac{1}{2}\cdot \:3\right)^3=\left(\frac{1}{2}\right)^3\cdot \:3^3$

$=-\left(\frac{1}{2}\right)^3\cdot \:3^3$

$=-\frac{1}{8}\cdot \:3^3$

$=-\frac{1}{8}\cdot \:27$

$=-\frac{27}{8}$