Question

Can someone help me out on this? I'm confused on what to do on this page. Can someone lend a hand?

Answer all the questions pls, 12-14, on the page, and give the step by step explanation as well ​

Answer 1

12)

$(a^3 b^4)^y~~ = ~~a^6 b^x\implies a^{3y} b^{4y}~~ = ~~a^6 b^x \\\\[-0.35em] ~\dotfill\\\\ a^{3y}=a^6\implies 3y=6\implies y=\cfrac{6}{3}\implies \boxed{y=2} \\\\\\ b^{4y}=b^x\implies 4y=x\implies 4(\stackrel{y}{2})=x\implies \boxed{8=x} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (a^3 b^4)^2~~ = ~~a^6 b^8~\hfill$

13)

$\left( \cfrac{r^y}{s^3} \right)^2~~ = ~~\cfrac{r^{10}}{s^x}\implies \cfrac{r^{2y}}{s^{3\cdot 2}}~~ = ~~\cfrac{r^{10}}{s^x}\implies \cfrac{r^{2y}}{s^6}~~ = ~~\cfrac{r^{10}}{s^x} \\\\[-0.35em] ~\dotfill\\\\ r^{2y}=r^{10}\implies 2y=10\implies y=\cfrac{10}{2}\implies \boxed{y=5} \\\\\\ s^6=s^x\implies \boxed{6=x} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \left( \cfrac{r^5}{s^3} \right)^2~~ = ~~\cfrac{r^{10}}{s^6}~\hfill$

Answer 2

Answer:

12) B^4 x 2 = B^8

13) (R^5 / S^3 )^2 = R^10 / S^6

14) Look below in the picture

                                                 

Step-by-step explanation:

12)  First we need to start by looking at the variables A and B. We see that we don't know both of the numbers (exponents) for variable B, but we do for variable A. the left A is raised to the 3rd, while the right A is raised to the 6th so since we have both A numbers, we will start with A. Then, with 2 in the square on the left, since that equals out the A variables on both sides to A^6. Then we would need to solve B^4 x 2 that will give you the answer to the square on the right. So we would have to multiply the 4 times 2 to get 8 and that would fill the square on the right side because A^3 x 2 = A^6

therefore B^4 x 2 = B^8 is or answer for this problem.

13) So the first thing we have to do is the Square on the bottom right side for the S variable or in other words, what is the answer to S^3 x2 =. If you got S^3 x 2 = S^6 you are correct. (Not the answer yet) so the answer for the bottom right square is 6. Now for the top left Square 3 times 2 equals 6 the parenthesis on the left are being squared or raised to the power of 2 so then for the top left square, if S^3 x 2 = S^6. Next we need to find out what R^10 Divided by 2 = equals to. If you said 5 amazing! Therefore for this question the answer is (R^5 / S^3 )^2 = R^10 / S^6.

14) Something you should remember when there's boxes is wherever you have the square box representation I am going to write it as a variable like w or y. Your first square is represented as "w" and the second square as y. Which would make it look like (w x 10^5)^2 = 9 x 10^y. So we had (w x 10^5)^2 so when you take the square root, it becomes just w x 10^5 which would make it look like (w x 10^5) = square root of (9 x 10^y). On the right hand side also yo have to do the square root . Square root (9 x 10^y) and square root of 9 is 3. Also, we have to leave the other term as is meaning as square root of 10^y okay now from this we can see that w = 3. We know y = 10. 10 is raised to 5 on the left side and raised to y/2 on the right side so 5 = y/2 from that we know y = 10 things circled in green have to be equal since the base is 10 on both sides.