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Exponents

Raising a Product to a Power

When a product is raised to a power, we can distribute that power through to each term in the product. That is,

(a*b)^n=a^n*b^n.

This is true for all kinds of exponents, positive and negative (and as we will see later, fractional).

Examples

(a*b)^3=a*b*a*b*a*b=a^3*b^3.

(x*y)^4=x*y*x*y*x*y*x*y=x^4*y^4.

(5*x)^2=5*x*5*x=(5^2)*x^2=25*x^2.

Look at these examples with positive powers:
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Exercise

 
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Working
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Now move onto some negative exponents.

Examples

(a*b)^(-4)=1/(a*b)^4=1/(a*b*a*b*a*b*a*b)=1/(a^4*b^4).

(3*y)^(-3)=1/(3*y)^3=1/(3*y*3*y*3*y)=1/(3^3*y^3)=1/(27*y^3).

Study some more examples with negative powers:
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Exercise

Practice your skills with these exercises.

   

Working space

  

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<< Raising One Power to Another | Exponents Index | Raising a Quotient to a Power >>

 
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