Question

How do you express `(-16a^ -3 b^ -5)/(2a^ -4 b^2)` with positive exponents?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(-16)/2(a^-3/a^-4)(b^-5/b^2) => -8(a^-3/a^-4)(b^-5/b^2)`

Next, use these rules for exponents to simplify the `a` term:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))` and `a^color(red)(1) = a`

`-8(a^color(red)(-3)/a^color(blue)(-4))(b^-5/b^2) =>`

`-8a^(color(red)(-3)-color(blue)(-4))(b^-5/b^2) =>`

`-8a^(color(red)(-3)+color(blue)(4))(b^-5/b^2) =>`

`-8a^color(red)(1)(b^-5/b^2) =>`

`-8a(b^-5/b^2)`

Now, use this rule for exponents to simplify the `b` term:

`-8a(b^color(red)(-5)/b^color(blue)(2)) =>`

`-8a(1/b^(color(blue)(2)-color(red)(-5))) =>`

`-8a(1/b^(color(blue)(2)+color(red)(5))) =>`

`-8a(1/b^7) =>`

`(-8a)/b^7`

Answer 2

`-(8a)/(b^7)`

Explanation:

`(-16a^ -3 b^ -5)/(2a^ -4 b^2)`

Use the rule for exponents: `a^-n=1/a^n`

and the rule `a^n/a^m=a^(n-m)`

`(-16a^ -3 b^ -5)/(2a^ -4 b^2)`

first let's simplify:

`(-16*a^ -3*b^ -5)/(2*a^ -4*b^2)`

`-8*a^(-3-(-4))*b^(-5-2)`

`-8*a^(-3+4)*b^(-7)`

`-8*a*b^(-7)`

Now move the negative exponents:

`-(8a)/(b^7)`

Answer 3

`(-16a^-3b^-5)/(2a^-4b^2)`

Group the like terms.

`=frac(-16)(2)*frac(a^-3)(a^-4)*frac(b^-5)(b^2)`

Use the rule `frac(x^p)(x^q)=x^(p-q)`

`=-8*a^(-3+4)*b^(-5-2)`

Simplify the exponents.

`=-8*a*b^-7`

Use the rule `x^-n=frac(1)(x^n)` to write it with positive exponents.

`=-8a*frac(1)(b^7)`

Simplify.

`=-frac(8a)(b^7)`