Answer: First option is correct.
Step-by-step explanation:
Since we have given that
![(\frac{2ab}{a^{-5}b^2})^{-3}](https://tex.z-dn.net/?f=%28%5Cfrac%7B2ab%7D%7Ba%5E%7B-5%7Db%5E2%7D%29%5E%7B-3%7D)
We will use law of exponents :
![(\frac{2ab}{a^{-5}b^2})^{-3}\\\\=(\frac{a^{-5}b^2}{2ab})^3\text{ }\because (a^m)^{-1}=\frac{1}{a^m}\\\\=\frac{a^{-15}b^{6}}{8a^3b^3}\text{ }\because (a^m)^n=a^{mn}\\\\=\frac{b^{6-3}}{a^{3+15}}\\\\=\frac{b^3}{8a^{18}}](https://tex.z-dn.net/?f=%28%5Cfrac%7B2ab%7D%7Ba%5E%7B-5%7Db%5E2%7D%29%5E%7B-3%7D%5C%5C%5C%5C%3D%28%5Cfrac%7Ba%5E%7B-5%7Db%5E2%7D%7B2ab%7D%29%5E3%5Ctext%7B%20%7D%5Cbecause%20%28a%5Em%29%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Ba%5Em%7D%5C%5C%5C%5C%3D%5Cfrac%7Ba%5E%7B-15%7Db%5E%7B6%7D%7D%7B8a%5E3b%5E3%7D%5Ctext%7B%20%7D%5Cbecause%20%28a%5Em%29%5En%3Da%5E%7Bmn%7D%5C%5C%5C%5C%3D%5Cfrac%7Bb%5E%7B6-3%7D%7D%7Ba%5E%7B3%2B15%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7Bb%5E3%7D%7B8a%5E%7B18%7D%7D)
So, the simplified form is
![\frac{b^3}{8a^{18}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E3%7D%7B8a%5E%7B18%7D%7D)
Hence, First option is correct.
Answer:
$4,880.80
Step-by-step explanation:
A = P(1 + r/n)^nt
Where,
A = future value
P = principal = $4,000
r = interest rate = 2% = 0.02
n = number of periods = 2
t = time = 10
A = P(1 + r/n)^nt
= 4000( 1 + 0.02/2)^2*10
= 4000(1 + 0.01)^20
= 4000( 1.01 )^20
= 4000(1.2202)
= 4,880.8
A = $4,880.80 to the nearest cents
.3125 expressed as a fraction is 5/16
Answer:
if im not missing it its..
Step-by-step explanation:
r = ![\frac{3t}{t - 1}](https://tex.z-dn.net/?f=%5Cfrac%7B3t%7D%7Bt%20-%201%7D)
multiply both sides of the equation by r - 3
t(r - 3 ) = r ( distribute and collect terms in r together )
tr - 3t = r
tr - r = 3t ( factor out r )
r(t - 1 ) = 3t ( divide both sides by r - 1 )
r = ![\frac{3t}{t - 1}](https://tex.z-dn.net/?f=%5Cfrac%7B3t%7D%7Bt%20-%201%7D)