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2 years ago

I cant remember how to do this

Mathematics

1 answer:

patriot [66]2 years ago

8 0

Okay let’s go through this together I’ll break it down.

2x+3/ x-2 = 38/12

Cross multiply
12(2x+3) = 38(x-2)
24x+36 = 38x-76
- 36= -36
—————————-
24x= 38x-112
-38x= -38x
———————-
-14x = -112
—————— divided
-14x = -14

X= 8

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$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

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Substitute $2^5$ for 32

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$\frac{a^m}{a^n} = a^{m-n}$

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