What is the simplest radical form of the expression?

1 answer:

8 0

$\bf (x^2y^8)^{\frac{2}{3}}\implies \left( x^{2\cdot \frac{2}{3}}y^{8\cdot \frac{2}{3}} \right)\implies x^{\frac{4}{3}}y^{\frac{16}{3}}\implies x^{\frac{3}{3}+\frac{1}{3}}y^{\frac{15}{3}+\frac{1}{3}}\implies x^{1+\frac{1}{3}}y^{5+\frac{1}{3}} \\\\\\ x^1\cdot x^{\frac{1}{3}}\cdot y^5\cdot y^{\frac{1}{3}}\implies x^1\cdot y^5\cdot x^{\frac{1}{3}}\cdot y^{\frac{1}{3}}\implies xy^5\sqrt[3]{x}\sqrt[3]{y}\implies xy^5 \sqrt[3]{xy}$

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Ray industries bought a touchscreen monitor for $1200 it is expected to depreciate at a rate of 25% per year what was the value

max2010maxim [7]

So for this problem, we will be using the exponential equation format, which is y = ab^x. The a variable is the initial value, and the b variable is the growth/decay.

Since our touchscreen starts off at a value of 1200, that will be our a variable.

Since the touchscreen is decaying in value by 25%, subtract 0.25 (25% in decimal form) from 1 to get 0.75. 0.75 is going to be your b variable.

In this case, time is our independent variable. Since we want to know the value 3 years from now, 3 is the x variable.

Using our info above, we can solve for y, which is the cost after x years.

$y=1200*0.75^3\\y=506$