Answer:
a. 10,000
b. 81
c. -8
d. 25
e. 1236
f. 8/27
g. 81/625
h. 1/32
i. 1/36
j. 1
k. 8
Step-by-step explanation:
How I got each of these answers:
a. 10^4
10 * 10 * 10 * 10
100 * 10 * 10
1000 * 10
10000
b. -3^4 (two negatives equal a positive)
-3 * -3 * -3 * -3
9 *-3 * -3
-27 * -3
81
c. -2^3
-2 * -2 * -2
4 * -2
-8
d. -5^2
-5 * -5
25
e. -6^4
-6 * -6 * -6 * -6
36 * -6 * -6
-216 * -6
1236
f. (2/3)^3
(2*2*2)/(3*3*3)
(4*2)/(9*3)
8/27
g. (-3/5)/4
(-3*-3*-3*-3)/(5*5*5*5)
(9*-3*-3)/(25*5*5)
(-27*3)/(125*5)
81/625
h. (1/2)^5
1/(2*2*2*2*2)
1/(4*2*2*2)
1/(8*2*2)
1/(16*2)
1/32
i. (-1/6)^2
(-1 * -1)/(6*6)
1/36
j. (2/5)^9 / (2/5)^9
(2^9)/(5^9) / (2^9)/(5^9)
(512/1953125) / (512/1953125)
1
k. -24t^4/-3t^4
(-24t^4)^1 * (1/-3t^4)
(-24)^1 * (t^4)^1 * (1/-3) * (1/t^4)
(-24)^1 * (1/-3)(t^4) * (1/t^4)
(-24)^1 * (1/-3) * t^4 * t^4(-1)
(-24)^1 * (1/-3) * t^4 * t^-4
(-24)^1 * (1/-3) * t^0
-24 * -1/3 * t^0
8t^0
8 * 1
8
