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## AmberlyKhan one year ago All exponent rules? Adding, subtracting, multiplying, dividing, etc...

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1. anonymous

You can only add and subtract like terms, meaning each term has the same variables to the same power. For example you can add and subtract $$2x^4$$ and $$-6x^4$$ by adding or subtracting the coefficients and leaving the exponents the same. Addition $2x^4+(-6x^4)=-4x^4$ Subtraction $2x^4-(-6x^4)=8x^4$

2. anonymous

With multiplication and division, the exponents change. Multiplication (multiply coefficients, add exponents) $x^mx^n=x^{m+n}$ Example $(8x^5y^7)(4x^3y^2)=32x^{5+3}y^{7+2}=32x^8y^9$ Division (divide coefficients, subtract exponents) $\frac{ x^m }{ x^n }=x^{m-n}$ Example$\frac{ 8x^5y^7 }{ 4x^3y^2 }=2x^{5-3}y^{7-2}=2x^2y^5$

3. anonymous

Power to a power (multiply the exponents) $(x^m)^n=x^{mn}$ Example $(x^3y^5)^2=x^{3*2}y^{5*2}=x^6y^{10}$ Negative exponents (take the reciprocal, change the exponent to positive) $x^{-m}=\left( \frac{ 1 }{ x } \right)^m$ Example $(3x)^-5=\left( \frac{ 1 }{ 3x } \right)^5$ $\left( \frac{ 1 }{ 2 } \right)^{-3}=2^3=8$ Anything to the 0 power is 1. $(x^4+7)^0=1$ $5(x^6y^3)^0=5*1=5$

4. anonymous

Rational exponents / Radicals $\sqrt[n]{x^m}=x^\frac{ m }{ n }$ Example $\sqrt{3x}=(3x)^\frac{ 1 }{ 2 }$ $\sqrt[4]{(12x)^5}=(12x)^\frac{ 5 }{ 4 }$

5. AmberlyKhan

Thanks! @peachpi

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