Answer:
0.001728 is the cube of [tex]\frac{3}{25}[/tex]
Step-by-step explanation:
0.001728 = [tex]\frac{1728}{1000000}[/tex]
break down each using LCD
1728 / 2 = 864
864 / 2 = 432
432 / 2 = 216
216 / 2 = 108
108 / 2 = 54
54 / 3 = 27
27 / 3 = 9
9 / 3 = 3
3 / 3 = 1
1000000 / 2 = 500000
500000 / 2 = 250000
250000 / 2 = 125000
125000 / 2 = 62500
62500 / 2 = 31250
31250 / 5 = 15625
15625 / 5 =3125
3125 / 5 =625
625 /2 = 125
125 / 5 =25
25 / 5 = 5
5 / 5 = 1
*don't forget to add another 2 for each group*
[tex]\frac{1728}{1000000}[/tex] = [tex]\frac{2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3}{2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5 * 5 * 5 * 5}[/tex]
= [tex]\frac{3 * 3 * 3}{5 * 5 * 5 * 5 * 5 * 5}[/tex]
= [tex]({\frac{3x^{3} }{5x^{3} * 5x^{3} })^{3}[/tex]
= [tex]\sqrt[3]{\frac{1728}{1000000} } = (\frac{3}{5 * 5} )^{3}[/tex]
=[tex]\sqrt[3]{\frac{1728}{1000000} } = \frac{3}{5 * 5}[/tex]
= [tex]\sqrt[3]{0.001728} = \frac{3}{25}[/tex]
