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April 19th, 2017, 06:59 AM  #1 
Newbie Joined: Apr 2016 From: England Posts: 13 Thanks: 2  Getting stuck simplifying equations with unknown values.
Simplify (t to the power of 3)to the power of 2 Simplify w to the power of 9/w to the power of 4 (thats a fraction) I have no idea where to start here as I've never really had to deal with simplifying powers. Any help would be massively appreciated! 
April 19th, 2017, 07:46 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,922 Thanks: 1518 
Do you mean ... $(t^3)^2$ or $t^{3^2}$. ? first one simplifies to $t^6$, second one is $t^9$ 
April 19th, 2017, 09:38 AM  #3 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
The laws of exponents for positive, real number a and real numbers b and c are: $\text {Law 1 is: } a^0 \equiv 1.$ $\text {Law 2 is: } a^1 \equiv a.$ $\text {Law 3 is: } a^{b} \equiv \dfrac{1}{a^b} \equiv \left ( \dfrac{1}{a} \right )^b.$ $\text {Law 4 is: } a^{(b+c)} \equiv a^b * a^c.$ $\text {Law 5 is: } a^{(bc)} \equiv \dfrac{a^b}{a ^c}.$ $\text {Law 6 is: } a^{(bc)} \equiv (a^b)^c.$ $\text {Law 7 is: } c \ne 0 \implies a^{(b \div c)} \equiv \sqrt[c]{a^b}.$ And obviously $b \div c = \dfrac{b}{c}.$ Once you memorize those seven laws, you can do this type of problem forever. If the base (a in the formulation above) is not positive, there are some special exceptions. Laws 1 and 3 do not apply to zero. Law 7 may not give a real number as an answer. Now you know virtually all you need to know about exponents in algebra. Last edited by JeffM1; April 19th, 2017 at 09:45 AM. 
April 19th, 2017, 11:11 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024 
Law 8 is use Google...


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