If f(x) = x^(-2/3), what is the value of f(8) ?

f(x) = x^(-2/3)

1

--------- = f(x) {made a positive exponent by moving into denominator}

x^(2/3)

1

--------- = f(8) {substituted 8 for x}

8^(2/3)

1

---------- = f(8) {8 to the two-thirds power is the same as the cube root of 8, squared}

(³√8)²

1

------ = f(8) {evaluated the cube root of 8 to be 2}

2²

1

--------- = f(x) {made a positive exponent by moving into denominator}

x^(2/3)

1

--------- = f(8) {substituted 8 for x}

8^(2/3)

1

---------- = f(8) {8 to the two-thirds power is the same as the cube root of 8, squared}

(³√8)²

1

------ = f(8) {evaluated the cube root of 8 to be 2}

2²

**1**

--- = f(8){squared the 2}--- = f(8)

**4**

or

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