Answer:
12) B^4 x 2 = B^8
13) (R^5 / S^3 )^2 = R^10 / S^6
14) Look below in the picture
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.