ANSWER
[tex] \\ [/tex]
[tex] \\ 3. \frac{5}{125} = \frac{1}{25} \\ [/tex]
Expand 125
[tex] \\ \frac{5}{5 \times 5 \times 5} \\ [/tex]
Cancel both same term then change it to one
[tex] \\ \frac{ \cancel{5}}{ \cancel{5} \times 5 \times 5} = \frac{1}{1 \times 5 \times 5} \\ [/tex]
Multiply the remaining digits of the denominator
[tex] \\ \frac{1}{1 \times 5 \times 5} = \boxed{\frac{1}{25}} \\ \\ [/tex]
[tex] \\ 4. \frac{ {x}^{7} }{ {x}^{8} } = \frac{1}{x} \\ [/tex]
Expand
[tex] \\ \frac{x \times x \times x \times x \times x \times x \times x}{x \times x \times x \times x \times x \times x \times x \times x} \\ [/tex]
Cancel all same terms
[tex] \\ \frac{ \cancel{x} \times\cancel{x} \times \cancel{x} \times \cancel{x} \times \cancel{x} \times\cancel{x} \times \cancel{x} }{\cancel{x} \times\cancel{x} \times\cancel{x} \times \cancel{x} \times \cancel{x} \times \cancel{x} \times\cancel{x} \times x } \\ [/tex]
Cancelled terms becomes one
[tex] \\ \small\frac{1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1}{1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times x} = \boxed{\frac{1}{x} } \\ \\ [/tex]
[tex] \\ 5 . \frac{ {y}^{8} }{ {y}^{16} } = \frac{1}{ {y}^{8} } \\ [/tex]
[tex] \\ \tiny \frac{y \times y \times y \times y \times y \times y \times y \times y}{y \times y \times y \times y \times y \times y \times y \times y \times y \times y \times y \times y \times y \times y \times y \times y} \\ [/tex]
Cancel all same terms
[tex] \\ \tiny \frac{ \cancel{y \times y \times y \times y \times y \times y \times y \times y}}{ \cancel{y \times y \times y \times y \times y \times y \times y \times y} \times y \times y \times y \times y \times y \times y \times y \times y} \\ [/tex]
Change the cancelled terms to 1
[tex] \\ \tiny\frac{1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1}{1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times y \times y \times y \times y \times y \times y \times y \times y} \\ [/tex]
Simplify
[tex] \\ \boxed{ \frac{1}{ {y}^{8} } } \\ \\ \\ \\ [/tex]
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