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Negative fractional indices

Combine reciprocals, powers and roots.

  • Check the brackets and the sign of the base before applying an index rule.
  • For a common base: multiplication adds indices, division subtracts them, and a power of a power multiplies them.
  • A negative index takes a reciprocal. A fractional index uses a root.

Example 1

Evaluate. Give an exact answer.

The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.

Example 2

Evaluate. Give an exact answer.

The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.

Your turn

Question 1

Evaluate. Give an exact answer.

Check answer
The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.
Question 2

Evaluate. Give an exact answer.

Check answer
The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.
Question 3

Evaluate. Give an exact answer.

Check answer
The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.
Question 4

Evaluate. Give an exact answer.

Check answer
The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.
Question 5

Evaluate. Give an exact answer.

Check answer
The denominator gives the root; the numerator gives the power. A negative index then takes the reciprocal.Evaluate the power or root.
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