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12345 [234]
3 years ago
9

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

Mathematics
2 answers:
Doss [256]3 years ago
8 0

<u>Answer:</u>

n = 10

<u>Step-by-step explanation:</u>

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

tino4ka555 [31]3 years ago
3 0

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



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<u>NOTE</u><u>;</u><u> </u><u>(</u><u>when </u><u>you </u><u>have </u><u>two </u><u>numbers </u><u>or </u><u>values </u><u> </u><u>remaining </u><u>instead</u><u> </u><u>of</u><u> </u><u>one </u><u>number,</u><u> </u><u>add </u><u>those </u><u>t</u><u>wo </u><u>numbers </u><u>and </u><u>divide</u><u> </u><u>by </u><u>2</u><u>)</u><u>.</u>

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Hope this helps.

Good luck ✅.

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