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Power of a monomial

Mathematics — first biennium · Monomials

Monomials · powers

The power acts on every factor

To raise a monomial to a power, raise the coefficient too, taking its sign into account, and multiply every exponent in the literal part by the outer exponent.

Formula matematica

(−2)³ = −8; (x²)³ = x⁶; y³ = y³.

Two rules together
Formula matematica
Formula matematica

The outer exponent acts on every factor of the monomial, not only on the variables.

What you need to know before the exercises

In this lesson: Raise a monomial to a power by applying the exponent to the coefficient and every factor in the literal part.

You can already assume: Multiplying monomials and laws of exponents.

Try it now

Reduce the power to normal form

Guided

Completed exercises: 0/5 · Correct on first attempt: 0

Guide
  1. Raise the coefficient, including its sign.
  2. Multiply every literal exponent by the outer exponent.
  3. Write one monomial in normal form.
Formula matematica

Write the result as you would on paper, for example −8x⁶y³.

Your competency map

What you need to know for Power of a monomial

ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.

Current topic Strong skill Review due Needs reinforcement To be mastered Optional support

Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.

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