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

3 Answers
Jun 23, 2018

Answer:

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

Answer:

#-(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)#