1. Simplify

(1/5)^3y=0.008 then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125

2. Originally Posted by devi
$\displaystyle (1/5)^3y=0.008$ then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125
solve for y in the first equation, and then plug in its value into the second to find its value

can you solve for y?

3. Originally Posted by Jhevon
solve for y in the first equation, and then plug in its value into the second to find its value

can you solve for y?
If that is the correct equation, then the answer wouldn't match any of the choices...

--Chris

4. Originally Posted by Chris L T521
If that is the correct equation, then the answer wouldn't match any of the choices...

--Chris
Perhaps (a) should've been 0.025

5. Originally Posted by Chris L T521
If that is the correct equation, then the answer wouldn't match any of the choices...

--Chris
The answer is given as 0.25
It is whole power 3y

6. Given: $\displaystyle (\frac{1}{5})^{3y}=0.008$

Take the log (unspecified base, but same base on both sides.) of both sides: $\displaystyle \log{(\frac{1}{5})^{3y}} = \log{0.008}$

Carry down 3y: $\displaystyle 3y \cdot \log{\frac{1}{5}} = \log{0.008}$

Divide by 3 and $\displaystyle \log{\frac{1}{5}}$ on both sides: $\displaystyle y = \frac{\log{0.008}}{3 \cdot \log{\frac{1}{5}}}$

y = ...

7. Originally Posted by devi
(1/5)^3y=0.008 then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125
Well, $\displaystyle \tfrac{1}{5}^{3y}=.008\implies \tfrac{1}{125}^y=.008$

However, $\displaystyle .008=\tfrac{1}{125}$, so we get the expression $\displaystyle \tfrac{1}{125}^y=\tfrac{1}{125}$

The only value of y that causes this expression to be true is $\displaystyle y=1$

But then $\displaystyle (0.025)^y\implies(0.025)^1=0.025$...

However, this isn't one of the solutions...

--Chris

8. Originally Posted by Chris L T521
Well, $\displaystyle \tfrac{1}{5}^{3y}=.008\implies \tfrac{1}{125}^y=.008$

However, $\displaystyle .008=\tfrac{1}{125}$, so we get the expression $\displaystyle \tfrac{1}{125}^y=\tfrac{1}{125}$

The only value of y that causes this expression to be true is $\displaystyle y=1$

But then $\displaystyle (0.025)^y\implies(0.025)^1=0.025$...

However, this isn't one of the solutions...

--Chris
i concur. the final answer is 0.025

9. Originally Posted by devi
(1/5)^3y=0.008 then $\displaystyle (0.025)^y$ will be
(a)0.25
(b)0.0625
(c)0.125
Solution:

$\displaystyle (1/5)^3y= 0.008$
$\displaystyle (1/5)^3y = (0.2)^3$
$\displaystyle (0.2)^3y = (0.2)^3$
y=1

Now
$\displaystyle (0.025)^y$
=$\displaystyle (0.025)^1$
=0.025