Question

How do you multiply `q^ { - 8} r ^ { 2} s ^ { - 7} t ^ { - 1} \cdot q ^ { - 1} r ^ { 2} s ^ { - 1} t ^ { - 9} \cdot q ^ { - 9} r s t ^ { - 4}`?

Answer 1

The answer is `r^5/(q^18s^7t^14)`.

Explanation:

Multiply:

`q^(-8)r^2s^(-7)t^(-1)*q^(-1)r^2s^(-1)t^(-9)*q^(-9)rst^(-4)`

Simplify multiplication.

`q^(-8)r^2s^(-7)t^(-1)q^(-1)r^2s^(-1)t^(-9)q^(-9)rst^(-4)`

Regroup like terms. `(a=a^1)`

`(q^-8q^(-1)q^(-9))(r^2r^2r^1)(s^(-7)s^(-1)s^1)(t^(-1)t^(-9)t^(-4))`

Apply product rule of exponents: `a^ma^n=a^(m+n)`.

`q^(-8+(-1)+(-9))r^(2+2+1)s^(-7+(-1)+1)t^(-1+(-9)+(-4))`

Simplify.

`q^(-18)r^5s^(-7)t^(-14)`

Apply negative exponent rule: `a^(-m)=1/a^m.`

`1/q^18xxr^(5)xx1/s^(7)xx1/t^14`

Simplify.

`r^5/(q^18s^7t^14)`