The expression
[tex] {4}^{5} \times {4}^{ - 7} \div {4}^{ - 2} [/tex]
is the same as
[tex] \frac{ {4}^{5} \times {4}^{ - 7} }{ {4}^{ - 2} } [/tex]
Which, if we switch the negative exponents, equals
[tex] \frac{ {4}^{5} \times {4}^{2} }{ {4}^{7} } [/tex]
And if we combine them, they equal
[tex] \frac{ {4}^{7} }{ {4}^{7} } [/tex]
Then we divide, and they equal
[tex] {4}^{0} [/tex]
