Answer:
50
Step-by-step explanation:
It ain't that hard. You just have to be careful and take things slow.... Here's how we can work it out:
[tex] \frac{ {8}^{ \frac{1}{3} } }{ {5}^{ - 2} } = \frac{ \sqrt[3]{ {8}^{1} } }{ \frac{1}{ {5}^{2} } } = \frac{ \sqrt[3]{ {2}^{3} } }{ \frac{1}{ {5}^{2} } } = \frac{2}{ \frac{1}{25} } = 2 \times 25 = 50[/tex]
I've used a couple things.
[tex] {8}^{ \frac{a}{b} } = \sqrt[b]{ {8}^{a} } [/tex]
[tex] {5}^{ - a} = \frac{1}{ {5}^{a} } [/tex]
and...
[tex] \frac{ \frac{a}{b} }{ \frac{c}{d} } = \frac{ad}{bc} [/tex]
In other words,
[tex] \frac{2}{ \frac{1}{25} } = \frac{ \frac{2}{1} }{ \frac{1}{25} } = \frac{2 \times 25}{1 \times 1} = 2 \times 25 = 50[/tex]
Hope I've helped ;)
