1

Problem

Simplify \$ (6^3)^-2 \$.

2

Step

Given expression

\$ (6^3)^-2 \$

3

Step

Apply the power of a power rule:

\$ (6^3)^-2 \$ = \$ 6^(3 \times -2)\$

4

Step

Calculate the exponent:

\$ 3 \times -2 \$ = -6

5

Step

Apply the negative exponent rule:

\$ 6^(-6) = 1/(6^6) \$

6

Solution

Final step is \$ 1/(6^6) \$.

7

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

8

Choice-A

This option represents a base 6 raised to the 7th power in the denominator, which is not the correct simplification of the original expression

Wrong \$ 1/(6^7) \$

9

Choice-B

This option shows a base 6 raised to the 4th power in the denominator, which is also incorrect for the given expression

Wrong \$ 1/(6^4) \$

10

Choice-C

This option indicates a base 6 raised to the 8th power in the denominator, which does not match the original simplification process

Wrong \$ 1/(6^8) \$

11

Choice-D

This option correctly shows a base 6 raised to the 6th power in the denominator, which matches our simplified result

Correct \$ 1/(6^6) \$

12

Step

Option

D

13

Sumup

Please Summarize Choices