Properties of exponents. Simplify, your answer should contain only positive exponents.

Question

1) 2m^2 ⋅ 2m^3

2) m^4 ⋅ 2m^−3 

3) 4r^−3 ⋅ 2r^2

4) 4n^4 ⋅ 2n^−3 

5) 2k^4 ⋅ 4k

6) 2x^3y^−3 ⋅ 2x^−1y^3 

7) 2y^2 ⋅ 3x

8) 4v^3 ⋅ vu^2 

9) 4a^3b^2 ⋅ 3a^−4b^−3

10) x^2y^−4 ⋅ x^3y^2 

11) (x^2)^0

12) (2x^2)^−4 

13) (4r^0)^4

14) (4a^3)^2 

15) (3k^4)^4

16) (4xy)^−1

Answer 1

add the exponents

multiply the coefficients

1) 2m^2(2m^3) = 4m^5

2) 2m

3) 8r^-1 = 8/r (just move r to the denominator and change its sign)

4) 8n

5) 8k^5

6) 4x^2 (add the y exponents to get 0, but y^0 =1, anyting to zero power=1)

7) 6xy^2

8) 4u^2v^4

9) 12/ab

10 x^5/y^2

11) 1 (anything to the zero power = 1)

12) 1/16x^8

13) 4^4 = 16^2 = 256

14) 4a^6

15) 3k^16

16) 1/4xy