Question

((2x^9)(y^n))((4x^2)(y^10))=(8x^11)(y^20)

Answer 1

We are given

$((2x^9)(y^n))((4x^2)(y^{10}))=(8x^{11})(y^{20})$

Firstly, we simplify left side

Left side is

$((2x^9)(y^n))((4x^2)(y^{10}))$

we will make all x terms together

and y terms together

$(2x^9)(4x^2)(y^n)(y^{10})$

$2\times 4(x^9)(x^2)(y^n)(y^{10})$

$8(x^9)(x^2)(y^n)(y^{10})$

we can multiply left side by using exponent rule

$a^m\times a^n=a^{m+n}$

$8(x^{9+2})(y^{n+10})$

$8(x^{11})(y^{n+10})$

now, we can set them equal

$(8x^{11})(y^{n+10})=(8x^{11})(y^{20})$

Since, both sides have x,y and 8

and both are equal

so, their exponent must be equal

so, exponent of y must also be equal

we get

$n+10=20$

$n=10$................Answer

Answer 2

Answer:

n = 10

Step-by-step explanation:

We are given an expression where a power n is unknown.

To find n, we will multiply all the terms at the left side and put them equal to the terms at the right side of the equal sign.

$((2x^9)(y^n)) ((4x^2)(y^{10} )) = (8x^11)(y^20)$

$(2x^9y^n)(4x^2y^{10} ) = 8x^{11} y^{20}$

$8x^{11} y^{n+10} = 8x^{11} y^{20}$

Now this is the most simplified form and we can see the same coefficients on each side so will put n+10 equal to its corresponding value.

$n+10 = 20$

$n = 20-10$

$n = 10$