How to solve 8 to the power of five thirds

Mathematics

1 answer:

Dmitriy789 [7]3 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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Lin is reading a 47 page book . She read the first 20 pages in 35 minutes. If she keeps reading at the same pace, how long will

Damm [24]

Answer:

It will take her 1 hour, 22 minutes, and 15 seconds.

Step-by-step explanation:

We can find how long it takes her to read one page if we take 35 divided by 20.

35/20 equals 1.75, which means it takes Lin 1.75 minutes to read 1 page.

If we multiple 1.75 times the 47 pages of the book, we get 82.25.

But, this does not mean that it takes Lin 82 minutes and 25 seconds to read the book. Since there are only 60 seconds in one minute, we must convert the .25 to seconds.

.25 is equivalent to 1/4, and 1/4 of 60 seconds is 15 seconds.

It would also look like this $\frac{1}{4} *\frac{60}{1} = \frac{60}{4} = 15$