Question

64x4y6=8xy5*.............. (4,6,5- степени) (-3ab3)2 *................=18 а в11 (3,2,11- степени) -х15у9= ............-х6у4 (15,9,6,4- степени) .........*(4х3у)2= 32х12у7 (3,2,12,7- степени)(3в3)2*...........=72в18 (3,2,18- степени)

Answer 1

$64 {x}^{4} {y}^{6} = 8x {y}^{5} \times 8 {x}^{3} y \\ ( - 3a {b}^{3} ) ^{2} \times 2 {a}^{ - 1} {b}^{5} = 9 {a}^{2} {b}^{6} \times 2 {a}^{ - 1} {b}^{5} = 18a {b}^{11} \\ - {x}^{15} {y}^{9} = {x}^{9} {y}^{5} \times (- {x}^{6} {y}^{4} )$
$32 {x}^{12} {y}^{7} = ...... \times (4 {x}^{3} y) ^{2} = ...... \times 16 {x}^{6} {y}^{2} = 2 {x}^{6} {y}^{5} \times 16 {x}^{6} {y}^{2} \\ 72 {b}^{18} = {(3 {b}^{3} )}^{2} \times ...... = 9 {b}^{6} \times 8 {b}^{12}$

Answer 2

To simplify the expressions, let's perform the indicated operations step-by-step:

1. 64x^4y^6 = 8xy^5 * ......... (4,6,5- powers)

To find the missing term, we need to equate the powers of x and y on both sides of the equation. We can do this as follows:

For x: 4 = 1 (from 8x) + x (unknown term) 4 = 1 + x x = 4 - 1 x = 3

For y: 6 = 5 (from 8xy^5) + y (unknown term) 6 = 5 + y y = 6 - 5 y = 1

So the missing term is 3x^3y.

Thus, the equation becomes: 64x^4y^6 = 8xy^5 * 3x^3y or simply: 64x^4y^6 = 24x^4y^6

2. (-3ab^3)^2 * ......... = 18a^11 (3,2,11- powers)

To find the missing term, we follow a similar approach:

For a: 2 = 1 (from -3a) + a (unknown term) 2 = 1 + a a = 2 - 1 a = 1

For b: 3 = 2 (from -3ab^3) + b (unknown term) 3 = 2 + b b = 3 - 2 b = 1

So the missing term is 1a^1b^1 or simply ab.

Thus, the equation becomes: (-3ab^3)^2 * ab = 18a^11

3. x^15y^9 = ......... - x^6y^4 (15,9,6,4- powers)

To find the missing term, we equate the powers of x and y on both sides:

For x: 15 = x (unknown term) + 6 (from -x^6y^4) x = 15 - 6 x = 9

For y: 9 = y (unknown term) + 4 (from -x^6y^4) y = 9 - 4 y = 5

So the missing term is x^9y^5.

Thus, the equation becomes: x^15y^9 = x^9y^5 - x^6y^4

4. (4x^3y)^2 = 32x^12y^7 (3,2,12,7- powers)

To find the missing term, we equate the powers of x and y on both sides:

For x: 2 * (3) = 12 (from 32x^12y^7) + x (unknown term) 6 = 12 + x x = 6 - 12 x = -6

For y: 2 * (1) = 7 (from 32x^12y^7) + y (unknown term) 2 = 7 + y y = 2 - 7 y = -5

So the missing term is -6x^(-6)y^(-5).

Thus, the equation becomes: (4x^3y)^2 = 32x^12y^7 - 6x^(-6)y^(-5)

5. (3b^3)^2 * ....... = 72b^18 (3,2,18- powers)

To find the missing term, we follow a similar approach:

For b: 2 * (3) = 18 (from 72b^18) + b (unknown term) 6 = 18 + b b = 6 - 18 b = -12

So the missing term is -12b.

Thus, the equation becomes: (3b^3)^2 * (-12b) = 72b^18

I've filled in the missing terms according to the patterns you provided. Please double-check the expressions for accuracy as mistakes can easily occur with complex equations. If you have any other questions or need further assistance, feel free to ask!