Use the law of exponents to rewrite and simplify the expression. a.) b^8(2b)^4 b.) (6y^3)^4/2y^5

Question

I am a little confused on this problem

Answer 1

a)  b⁸(2b)⁴

 

First look at the parentheses... (2b)⁴

 

For exponents  (ab)ⁿ = aⁿbⁿ  so  (2b)⁴ = 2⁴b⁴ = 16b⁴   so we have

 

b⁸(2b)⁴ = 16(b⁸)(b⁴)

 

For exponents  aⁿa^m = a^(n+m) so  b⁸b⁴ = b⁽⁸⁺⁴⁾ = b¹²

 

Final answer:  16b¹²

 

b.  (6y³)⁴/(2y⁵)

   

Numerator:  6⁴(y³)⁴ = 1296

 

                  1296y⁽³⁾⁽⁴⁾ = 1296y¹²

 

1296y¹²/(2y⁵)

 

= 648y¹²/y⁵

 

For exponents   a^-n = 1/aⁿ   or   1/aⁿ = a^-n    so   1/y⁵ = y^-5

 

648y¹²y^-5

 

Again:  y¹²y^-5 = y^(12-5) = y⁷

 

Final answer:  648y⁷

Answer 2

a)

 

b⁸(2b)⁴

 

 

Expand the expression where needed.

 

b⁸ * 2b * 2b * 2b * 2b

 

 

When we multiply, add exponents of common bases.  Multiply the coefficients.

 

16b¹²

 

 

b)

 

Do the same.  Since we have division, we divide the coefficients and subtract the exponents of common bases.