how to simplify 2b^2*(-2b^4)^-2

Question

please help me with this math problem

Answer 1

2(b^2)*( (-2)(b^4) )^(-2)

 

= 2(b^2)*((-2)^(-2))*(b^4)^(-2)

 

= 2(b^2)*(1/4)*b^(-8)

 

= (1/2) b^(-6)

 

= 1/(2b^6)

Answer 2

Hi!

 

Vivian gave a great answer, but I would go one more step.  I tell my students that negative signs in exponents are like eviction notices - you have to move to the other side of the fraction bar.  The b^-6 would move to the denominator, with a final answer of -4/b⁶.  I hope this helps!

Kim

 

Answer 3

Hi Anna;

2b^2*(-2b^4)^-2

Let's begin with the parenthetical...

(-2b⁴)^-2

(4)(-2)=-8

(-2b^-8)

(-2)^-2=1/(-2²)=1/4

2b²[(1/4)b^-8]

(2)(1/4)=1/2

(b²)(b^-8)=b^-6

(1/2)b^-6