#5.
a. False
1296 does not equal 4096
b. True
5^2 / 5^3 = 1/5^1 = 1/5
c. True
6^12 = 6^12
d. True
3^2 / 3^7 = 3^2 x 1 / 3^7 = 3^2 x 3^-7
e. False
1 / 8^-4 = 8^4
f. False
4^10 / 4^5 = 4^5
#6.
3000 = 3 x 10^3
300 = 3 x 10^2
3 = 3 x 10^0
0.3 = 3 x 10^-1
0.03 = 3 x 10^-2
0.003 = 3 x 10^-3
The exponent is the place value. 3000 is thousands, and has 3 zeroes in the exponent. 300 is hundreds, and has 2 zeroes in the exponent. 0.3 is in the tenths place, and ten has 1 zero. But decimals get smaller, which is why we use the negative exponents.
Hope this helps!