So in this question, I got $25b^8$, though my teacher marked it wrong and said it was $5b^8$, he said don't multiply the bases. But $5$ is not the base, $b$ is the base and $5$ is the coefficient. I am confused, I checked my word in a calculator and got $25b^8$. Help please
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Welcome to Math SE! Please use MathJax to format your posts. – Aniruddha Deb Oct 26 '20 at 13:52
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1I would say that $(5b^4)^2$ is definitely equal to $25 b^8$ ... – Matti P. Oct 26 '20 at 13:52
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Yeah so my teacher is wrong? – Jason Oct 26 '20 at 13:53
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1It all hangs on where the left bracket was in the problem. If it was, as you say, $(5b^4)^2$ then you are right. If it was $5(b^4)^2$, then your teacher is right. – Oct 26 '20 at 13:57
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Thanks everyone – Jason Oct 26 '20 at 14:13
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1The answer is definitely $25b^8$. This kind of thing really bothers me. How can a teacher make a mistake like this? I'd like to know the resolution to this Jason if you get an update from the teacher. – Ameet Sharma Oct 26 '20 at 14:19
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1I am almost sure that your exercise was $5(b^4)^2$. If not, change teacher ASAP! – Raffaele Oct 26 '20 at 14:22
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Jason. Welcome to StackExchange! First, thanks for following the guidelines on posting your problem (i.e. explain the problem and show your work).
I would argue that you are correct (my background is a BS, almost MS in math and candidacy for a BSE in Secondary Education Mathematics). Here's why:
Do you recall the term monomial? By definition, this is a one-term polynomial (it just has a variable raised to a power and a coefficient).
In our case, our monomial is $(5b^4)^2$. Since this monomial is raised to the second power, we interpret this as $5b^4\cdot5b^4=(5\cdot5)\cdot(b^4\cdot b^4)=25\cdot b^{4+4}=25\cdot b^8=25b^8$.
This website further explains how to solve problems of this nature should the teacher refuse both of our explanations. (If your teacher argues these are not of the form (coefficient$\cdot$variable$^{power}$)$^{power}$, then remind them you can rewrite it as I did. Best of luck!
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Thank you so much everybody! Yeah, this isn't the first mistake he made, I am thinking about what I should do from this point on. I appreciate all your help! – Jason Oct 28 '20 at 02:12