I Don't understand these problems!!! Can Anybody HELP!!!?

Question

( ^ = to the power of )

1. 3x^3 y^4 z^-2
----------------------
6x^-1 y^3 z^-3

2. 2^2
--------------
(3/2) ^-2 hint: ( 3/2 means 3 over 2 )

3. (4y)^7
--------------
(4y)^3

4. (2x^5)^3 (-3x^4)^3

5. 7(x^4)^5 (-4x^2)^2

6. ( 4x^3 )^3 hint: (parentheses mean the the whole equation ^3)
( ------ )
( 2y^2 )

7. ( 5x^3 )^2
-----------------
( 5xy^2 )^3


For questions 14 and 15, help me simplify the rational expressions.

14. -x^2 + 10x - 21
-----------------------------
-x^2 +23x - 14

15. 28x^2 - 29^x + 6
-----------------------------
- 28x^2 + 50x - 12

Answer 1

Hi Dear ;
{ (a ^ n ) * ( a ^ m ) = a ^ ( n + m )
(a ^ n ) / ( a ^ m ) = a ^ ( n - m )
a ^ -n = 1 / a ^ n } ....

■ Part 1
(3x^3 y^4 z^-2) / (6x^-1 y^3 z^-3) =
[ 3 / 6 ] * [ x ^3 / 6 x^ -1 ] * [ y ^ 4 / y ^ 3 ] * [ z ^ -2 / z ^ - 3 ] =
1/2 * [ x ^ 3 - (-1) ] * [ y ^ ( 4 - 3) ] * [ z ( -2 - ( -3)) ] =
1/2 ( x ^4 y z )

■ Part 2
(2^2) / (3/2) ^-2 =
{ 2 ^2 = 4 , (3/2) ^-2 = (2 /3) ^ 2 = 4 / 9 } ..
4 / (4 / 9) = ( 9 * 4 ) / 4 { cancel 4 }
2^2 / (3/2) ^-2 = 9

■ Part 3
(4y)^7 / (4y)^3 =
[ 4 ^ 7 * y ^ 7 ] / [ 4 ^ 3 * y ^ 3 ] =
[ 4 ^ (7 - 3) ] * [ y ^ ( 7 - 3)] =
(4 ^ 4) * (y ^ 4) = 256 y ^ 4

■ Part 4
(2x^5)^3 (-3x^4)^3 =
[ (2 ^ 3) * (x ^ ( 5 * 3 )) ] * [ (- 3 ^ 3) * ( x^ ( 4 * 3 ) ] =
[8 x ^ 15] * [ -27 x ^ 12 ] =
[ 8 * -27 ] * [ x ^ (15 + 12 ) ] =
- 216 ^ 27

■ Part 5
7(x^4)^5 (-4x^2)^2 =
[ 7 * ( x ^ ( 4 * 5 )] * [ -4 ^ 2 * (x ^ 2 * 2 ) ] =
[ 7 * x ^ 20 ] * [ 16 * x ^4] =
[ 7 * 16 ] * [ x ^ (20 + 4)] =
112 x ^ 24

■ Part 6
( 4x^3 )^3 / ( 2y^2 ) =
[ (4 ^ 3) * ( x ^ ( 3 * 3) ] / 2 y ^2 =
64 x ^ 9 / 2 y ^ 2 =
(64 / 2) * (x ^ 9 / y ^ 2) =
(32 x ^ 9) / y ^ 2

■ Part 7
( 5x^3 )^2 / ( 5xy^2 )^3 =
[ (5 ^ 2) * ( x ^ ( 3 * 2)] / [ ( 5 ^3) * (x ^ 3) * ( y ^ ( 2 * 3) ]
[ 25 x ^6] / [ 125 * x ^3 * y ^ 6 ] =
[ 25 / 125 ] * [ x ^ (6 - 3)] * [ 1 / y ^ 6]
( x ^ 3) / 5 y ^ 6

■ Part 8
-x^2 + 10x - 21 -x^2 +23x - 14 =
[ -x^2 -x^2 ] + [ 10x + 23x ] + [ -21 - 14] =
- 2x ^2 + 33x - 35

■ Part 9
28x^2 - 29^x + 6 - 28x^2 + 50x - 12 =
[ 28x^2 - 28x^2 ] + [- 29x + 50x ] + [ 6 - 12 ] =
21 x - 6

Good Luck dear ♣

Answer 2

1. 3x^4
2 9
3 4y^4
4. -6x^15
oh. So goes the answers. You are one more of the lazy lot.

Oh my god you are the same gu(al)y again. Shame Shame!

Answer 3

i like powers of two. 4^x = one million/sixty 4 2^(2x) = 2^(-6) This works because of the fact the exponents have a similar base. 2x = -6 x = -3 you ought to try this with one fewer step via doing it in powers of four, yet I desire 2.

Answer 4

Why don't you just drop the course. You've already failed it. Getting over on your teacher(s) may seem cool to you now, but all you are really doing is making yourself unemployable.

Answer 5

Thanks for all the hints, I have them all figured out

Answer 6

14_(-x+3)(x-7)
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