Question

Can someone please help me with this??

Answer 1

12. v = 0

13. b = 9

14. y = 5

15. z = -8

16. n = -m and n ≠ 0 and m ≠ 0

17. x = 3

Explanation:

`12.\ a^v=1\to a^v=a^0\to v=0\\\\\text{because}\ a^0=1\ \text{for any}\ a\\eq0.\\\\13.\ \ b^(-w)=(1)/(b^9)\to (1)/(b^w)=(1)/(b)\to b=9\\\\\text{because}\ a^(-n)=(1)/(a^n)\ \text{for any}\ a\\eq0\\\\14.\ (3^3)/(3^y)=(1)/(9)\to(3^3)/(3^y)=(3^0)/(3^2)\to 3-y=-2\to y=5\\\\\text{used}\ (a^m)/(a^n)=a^(n-m)\\\\15.\ 5^8\cdot5^z=1\to5^(8+z)=5^0\to8+z=0\to z=-8\\\\\text{used}\ a^n\cdot a^m=a^(n+m)`

`16.\ 7^n\cdot 7^m=1\to7^(n+m)=7^0\to n+m=0\to n=-m\\\\17.\ (3^x\cdot2^2)/(3^4)=(4)/(3)\to3^(x-4)\cdot2^2=3^(-1)\cdot2^2\to x-4=-1\to x=3`