Question

Simplify ^3 sq try (-0.05)^24

Answer 1

Answer:

As

• $\sqrt[3]{\left(-0.05\right)^{24}}=0.05^8$

so option D is correct.                    

Step-by-step explanation:

Given the expression

$\sqrt[3]{\left(-0.05\right)^{24}}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}$

$\sqrt[3]{\left(-0.05\right)^{24}}=\left(\left(-0.05\right)^{24}\right)^{\frac{1}{3}}$

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

                  $=\left(-0.05\right)^{24\cdot \frac{1}{3}}$

                  $=\left(-0.05\right)^8$  

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

                  $=0.05^8$

Hence, the simplification will be:

$\sqrt[3]{\left(-0.05\right)^{24}}=0.05^8$

Therefore, option D is correct.