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Unit 5.1 Exponents

Exponents

Product Rule

To multiply the same bases with different exponents, add the exponents

xa · xb= x(a+b)

Product Rule

x5 · x6 = x(5+6) = x11

Quotient Rule

To divide the same base with different exponents, subtract the exponents 

[latex]\frac{x^a}{x^b}[/latex]= x(a – b)

Quotient Rule

[latex]\frac{x^5}{x^3}=x^{5-3}=x^2[/latex]

Power Rule

When you have a power to a power, multiply the powers

(xa)b = xa · b

Power Rule

(x3)4 = x3 · 4 = x12

Power of a Product

Distribute the exponent across each term of the monomial

(xy)a = xaya

Power of a Product

(xy)5 = x5y5

This law also allows you to factor out exponents

x8y4 = (x2y)4

Power of a Quotient

Distribute the exponent to both the numerator and denominator

[latex]\left(\frac{\mathrm{x}}{\mathrm{y}}\right)^\mathrm{a}\mathrm{=} \frac{x^a}{y^a}[/latex]

Power of a Quotient

[latex]\left(\frac{\mathrm{x}}{\mathrm{y}}\right)^\mathrm{2}\mathrm{=} \frac{x^2}{y^2}[/latex]

Zero Exponent Law and Identity Law

Zero Exponent Law: Any value to a 0 exponent is equal to 1

Identity Law: Any value with an exponent of 1 is equal to that value

x0 = 1

x1 = x

Negative Exponent Rule

Any value to a negative exponent is the reciprocal of that number

x-1 =[latex]\frac{1}{x}[/latex]

Negative Exponent Rule

Example 1:

[latex]\mathrm{x}^{\mathrm{-4}}\mathrm{=\ }\frac{\mathrm{1} }{\mathrm{x}^\mathrm{4}}[/latex]

Example 2:

[latex]\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{-4}}}\mathrm{\ =\ }x^4[/latex]

 

 

 

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