How to solve 8 to the power of five thirds

Mathematics

1 answer:

Dmitriy789 [7]2 years ago

4 0

$8^\frac{5}{3}=8^{1\frac{2}{3}}=8^{1+\frac{2}{3}}=8\cdot8^\frac{2}{3}=8\sqrt[3]{8^2}=8\sqrt[3]{64}=8\cdot4=32\\\\Used:\\\\a^n\cdot a^m=a^{n+m}\\\\a^\frac{m}{n}=\sqrt[n]{a^m}\\---------------------------------\\Other\ method\\\\8=2^3\\\\8^\frac{5}{3}=(2^3)^\frac{5}{3}=2^{3\cdot\frac{5}{3}}=2^5=32\\\\Used:\\\\(a^n)^m=a^{n\cdot m}$

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This monitor has a diagonal length of 19 inches and an aspect ratio of 5:4. What are the width and height of the monitor? Round

nasty-shy [4]

<em>Rounded to the nearest tenth of an inch the Witdth of the monitor is 14.8 inches while the Height of the monitor is 11.9 inches.</em>

<h2>Explanation:</h2><h2 />

The aspect ratio is defined as:

<em>"The proportional relationship between the width and height of an image"</em>

It is usually expressed in a mathematical language as:

$x:y \\ \\ x: \ Width \\ \\ y: \ Height$

So, it is true that:

$x:y=5:4 \\ \\ or: \\ \\ \frac{x}{y}=\frac{5}{4} \\ \\ \therefore x=\frac{5y}{4}$

In this case, we know that the monitor has a diagonal length (D):

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So, by Pythagorean theorem:

$D^2=361 \\ \\ 361=x^2+y^2 \\ \\ Since \ x=\frac{5y}{4}$

$D^2=361 \\ \\ 361=x^2+y^2 \\ \\ Since \ x=\frac{5y}{4} \\ \\ 361=\left(\frac{5y}{4}\right)^2+y^2 \\ \\ 361=\frac{25y^2}{16}+y^2 \\ \\ \frac{41}{16}y^2=361 \\ \\ y^2=\frac{261\times 16}{41} \\ \\ y=\sqrt{140.87} \\ \\ y=11.869in$

Finding x:

$x=\frac{5(11.869)}{4} \\ \\ x=14.836in$

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<h2>Learn more:</h2>

Pythagorean Theorem: brainly.com/question/10182890

#LearnWithBrainly

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Step-by-step explanation:

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