Question

3^-6 x (3^4 / 3^0)^2

Answer 1

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

Answer 2

Answer:

9

Step-by-step explanation:

${3}^{ - 6} {\bigg( \frac{ {3}^{4} }{ {3}^{0} } \bigg)}^{2} \\ \\ = {3}^{ - 6} {\bigg( \frac{ {3}^{4} }{ 1 } \bigg)}^{2} ( \because \: {a}^{0} = 1) \\ \\ = {3}^{ - 6} {( {3}^{4} )}^{2} \\ \\ = {3}^{ - 6} {3}^{8} \\ \\ = {3}^{ - 6 + 8} \\ \\ = {3}^{2} \\ \\ = 9$