1

Problem

Simplify the expression \$((1/2) x^(3))^-2 \$.

2

Step

Given expression

\$( (1/2) x^(3) )^-2 \$

3

Step

Apply the negative exponent rule:

\$( (1/2) x^(3) )^-2 \$

\$1/(((1/2) x^(3))^2 )\$

4

Step

Simplify the expression inside the parentheses

\$(((1/2) x^(3))^2)\$

=\$(1/2)^2 \times (x^3)^2\$

=\$(1/4) \times x^6\$

5

Step

Invert the fraction:

\$1/((1/4) \times x^6)\$

6

Step

Simplify by multiplying the numerator and denominator by the reciprocal of the fraction

\$4/(x^6) \$

7

Solution

So, the simplified expression is \$4/(x^6) \$.

8

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

9

Choice-A

This option is incorrect because it suggests the exponent of x is 5 instead of 6

Wrong \$4/(x^5) \$

10

Choice-B

This option is incorrect because it suggests the numerator is 5 instead of 4

Wrong \$5/(x^6) \$

11

Choice-C

This option is incorrect because it suggests the numerator is 5 and the exponent of x is 5, neither of which is correct

Wrong \$5/(x^5) \$

12

Choice-D

This option is correct because it matches the simplified result

Correct \$4/(x^6) \$

13

Step

Option

D

14

Sumup

Please Summarize Choices