How do you simplify $(8r^-5s^-4)/(6qr^6s^-7)$ ?

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Answer 1 · 2017-03-18T17:38:38

$(4s^3)/(3qr^11)$

Using the Index law $a^(-n)=1/a^n$ , and conversely $1/a^(-n)=a^n$ , swap around the values so that they all have positive indices:

$(8s^7)/(6qr^5r^6s^4)$

Using the index law $a^m+a^n=a^(m+n)$ , you can simplify $r$ :

$(8s^7)/(6qr^(5+6)s^4)=(8s^7)/(6qr^(11)s^4)$

Using the index law $a^m/a^n=a^(m-n)$ gives

$(8s^(7-4))/(6qr^(11))=(8s^3)/(6qr^(11))$

Reduce:

$(cancel8^color(red)(4)s^3)/(cancel6^color(red)(3)qr^(11))=(4s^3)/(3qr^(11))$

How do you simplify (8r^-5s^-4)/(6qr^6s^-7)(8r^-5s^-4)/(6qr^6s^-7)?