Answer:
9 x
Step-by-step explanation:
Simplify the following:
((3^4/3^0)^2 x)/(3^6)
Hint: | Compute 3^6 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.
3^6 = (3^3)^2 = (3×3^2)^2:
((3^4/3^0)^2 x)/((3×3^2)^2)
Hint: | Evaluate 3^2.
3^2 = 9:
((3^4/3^0)^2 x)/((3×9)^2)
Hint: | Multiply 3 and 9 together.
3×9 = 27:
((3^4/3^0)^2 x)/(27^2)
Hint: | Evaluate 27^2.
| 2 | 7
× | 2 | 7
1 | 8 | 9
5 | 4 | 0
7 | 2 | 9:
((3^4/3^0)^2 x)/729
Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to 3^4/3^0.
Combine powers. 3^4/3^0 = 3^(4 + 0):
((3^4)^2 x)/729
Hint: | For all positive integer exponents (a^n)^m = a^(n m). Apply this to (3^4)^2.
Multiply exponents. (3^4)^2 = 3^(4×2):
(3^(4×2) x)/729
Hint: | Multiply 4 and 2 together.
4×2 = 8:
(3^8 x)/729
Hint: | Compute 3^8 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.
3^8 = (3^4)^2 = ((3^2)^2)^2:
(((3^2)^2)^2 x)/729
Hint: | Evaluate 3^2.
3^2 = 9:
((9^2)^2 x)/729
Hint: | Evaluate 9^2.
9^2 = 81:
(81^2 x)/729
Hint: | Evaluate 81^2.
| | 8 | 1
× | | 8 | 1
| | 8 | 1
6 | 4 | 8 | 0
6 | 5 | 6 | 1:
(6561 x)/729
Hint: | In (x×6561)/729, divide 6561 in the numerator by 729 in the denominator.
6561/729 = (729×9)/729 = 9:
Answer: 9 x
