Question

How do you simplify `\frac { a b ^ { 7} z ^ { 6} } { a ^ { 5} b ^ { 4} }`?

Answer 1

`(b^3z^6)/a^4`

Explanation:

Exponential division rule: `x^a/x^b=x^(a-b)`
`\therefore\frac { a b ^ { 7} z ^ { 6} } { a ^ { 5} b ^ { 4} }=a^((1-5))b^((7-4))z^6=a^(-4)b^(3)z^6`

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Negative exponent rule: `x^(-c)=1/x^c`
`\thereforea^(-4)b^(3)z^6=1/a^4b^3z^6=\color(steelblue)((b^3z^6)/a^4)`