Entrance examination to Stanford University

how to solve 4 power K is equal to 1 by K find the value of K so we have 4 power K is equal to 1 by K now uh multiply by power of 1 by K in both sides so multiply by power of 1 by K multip by power of 1 by K now here I can apply this exponential rule that a power M bracket power n is equal to a power of M * n that means it will be MN so according to this formula I can write here four uh 4 power of K * on by K then is equal to 1 by K bracket power of 1 by K now we see this K this K will be cancel so you have 4 power one is same as 4 is equal to 1 by K bracket power of 1 by K now let 1 by K is substituted by y so our equation will be y power Y is equal to 4 is same as 2 power 2 now here you can apply this rule a power a is equal to n^ n so a will be equal to n where n is greater than or equal to 1 so according to this rule we can compare here y will be equal to 2 but remember that uh let on by K is substituted by y so y that means it will be 1 by K is equal to 2 now here you can apply cross multiply so uh I can write here K multip by 2 that means it will be 2 K is equal to 1 * by 1 that means it will be one here 2 is same as 2 by 1 so K * 2 it will be 2 K is equal to 1 * 1 that means one now now we need the value of uh K so we divided by two in both sides so divided by two divided by two now we see uh this two this two will be cancel so we have K will be equal to uh 1 by 2 so 1 by two this is the value of K so this is our final answer after that how to solve x power x power 3 is equal to 36 find the value of x so we have X power x power 3 then is equal to 36 is same as 6 power 2 now we have X power x power 3 is equal to 6^ 2 now uh we multiply by power of three in both sides so multiply by power of three multiply by power of three now x^ 3 then bracket uh bracket power of X Cub according to this rule a power n braet power n is equal to a power n bracket power M then is equal to 6 power of 2 * 3 that me it will be six now uh I can write here x^ 3 will be equal to 6 according to this rule a power a is equal to n^ n so a will be equal to n where n is greater than or equal to 1 now we need the value of x so we multiply by power of 1 by 3 in both sides so multiply by power of 1 by 3 multiply multip power of 1 by 3 so this three this three will be cancelled so here x^ 1 is same as X is equal to 6 power of 1x 3 can be written as cube root of 6 so cube root of 6 this is the value of x so this is our final answer