Answer:
As
- [tex]\sqrt[3]{\left(-0.05\right)^{24}}=0.05^8[/tex]
so option D is correct.
Step-by-step explanation:
Given the expression
[tex]\sqrt[3]{\left(-0.05\right)^{24}}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
[tex]\sqrt[3]{\left(-0.05\right)^{24}}=\left(\left(-0.05\right)^{24}\right)^{\frac{1}{3}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}[/tex]
[tex]=\left(-0.05\right)^{24\cdot \frac{1}{3}}[/tex]
[tex]=\left(-0.05\right)^8[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}[/tex]
[tex]=0.05^8[/tex]
Hence, the simplification will be:
[tex]\sqrt[3]{\left(-0.05\right)^{24}}=0.05^8[/tex]
Therefore, option D is correct.
