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

3 Answers
Jun 23, 2018

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

Jun 23, 2018

-(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)

Jun 23, 2018

(-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)