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geniusboy [140]
3 years ago
14

Simplify the expression. (16y^5/4y^3)^1/2

Mathematics
1 answer:
Soloha48 [4]3 years ago
5 0
\bf a^{\frac{ n}{ m}} \implies  \sqrt[ m]{a^ n} 
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
\left( \cfrac{16y^5}{4y^3} \right)^{\frac{1}{2}}\implies \left( \cfrac{4^2y^5}{2^2y^3} \right)^{\frac{1}{2}}\impliedby \textit{let's distribute the exponent}

\bf \left( \cfrac{4^{2\cdot \frac{1}{2}}y^{5\cdot \frac{1}{2}}}{2^{2\cdot \frac{1}{2}}y^{3\cdot \frac{1}{3}}} \right)\implies \cfrac{4^1y^{\frac{5}{2}}}{2^1y^1}\implies \cfrac{4y^{\frac{5}{2}y^{-1}}}{2}\implies \cfrac{4y^{\frac{5}{2}-1}}{2}\implies \cfrac{4y^{\frac{3}{2}}}{2}
\\\\\\
\cfrac{2y^{\frac{3}{2}}}{1}\implies 2\sqrt[2]{y^3}\implies 2\sqrt{y^{2+1}}\implies 2\sqrt{y^2y}\implies 2y\sqrt{y}
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We have been given that an account is opened with a balance of $3,000 and relative growth rate for a certain type of mutual fund is 15% per year.  

In order to tackle this problem we have to find the value of mutual fund after 5 years. For our purpose we will use compound interest formula.

A=P(1+r)^{t} ,where A= amount after t years, P= principal amount, r= interest rate (decimal) and t= number of years.

After substituting our given values in above formula we will get

A=3000(1+.15)^{5}

Now we will solve for A

A=3000(1+.15)^{5}=3000(1.15)^{5}\\ A=3000\cdot (2.011357187)=6034.07

Therefore, after 5 years mutual fund is worth $6034.07.


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See below.

Step-by-step explanation:

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