Question

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

Answer 1

Answer: -27/8

Explanation:

`\left(-(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(-(1)/(2)\cdot \:3\right)^3=-\left((1)/(2)\cdot \:3\right)^3`

`=-\left((1)/(2)\cdot \:3\right)^3`

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

`\left((1)/(2)\cdot \:3\right)^3=\left((1)/(2)\right)^3\cdot \:3^3`

`=-\left((1)/(2)\right)^3\cdot \:3^3`

`=-(1)/(8)\cdot \:3^3`

`=-(1)/(8)\cdot \:27`

`=-(27)/(8)`