Looking for the area of a regular figure would be taking the longest side and the shortest side and multiply
Answer:
14
Step-by-step explanation:
Multiply the exponents together
Convert the fractions to decimals:
3/5=0.6
4/5=0.8
You have to find 2 fractions between these 2 numbers. You could pick anything.
7/10= 0.7 = less than 0.8 but greater than 0.6
75/100=0.75 = less than 0.8 but greater than 0.6
Hope this helps
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Answer:
![\frac{\sqrt[3]{16y^4}}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B16y%5E4%7D%7D%7Bx%5E2%7D)
Step-by-step explanation:
The options are missing; However, I'll simplify the given expression.
Given
![\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B32x%5E3y%5E6%7D%7D%7B%5Csqrt%5B3%5D%7B2x%5E9y%5E2%7D%20%7D)
Required
Write Equivalent Expression
To solve this expression, we'll make use of laws of indices throughout.
From laws of indices ![\sqrt[n]{a} = a^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
So,
gives
![\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B%2832x%5E3y%5E6%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B%282x%5E9y%5E2%29%5E%5Cfrac%7B1%7D%7B3%7D%7D)
Also from laws of indices
![(ab)^n = a^nb^n](https://tex.z-dn.net/?f=%28ab%29%5En%20%3D%20a%5Enb%5En)
So, the above expression can be further simplified to
![\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}](https://tex.z-dn.net/?f=%5Cfrac%7B%2832%5E%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%2A%5Cfrac%7B1%7D%7B3%7D%7Dy%5E%7B6%2A%5Cfrac%7B1%7D%7B3%7D%7D%29%7D%7B%282%5E%5Cfrac%7B1%7D%7B3%7Dx%5E%7B9%2A%5Cfrac%7B1%7D%7B3%7D%7Dy%5E%7B2%2A%5Cfrac%7B1%7D%7B3%7D%7D%29%7D)
Multiply the exponents gives
![\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}](https://tex.z-dn.net/?f=%5Cfrac%7B%2832%5E%5Cfrac%7B1%7D%7B3%7Dx%2Ay%5E%7B2%7D%29%7D%7B%282%5E%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%7D%2Ay%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%7D)
Substitute
for 32
![\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}](https://tex.z-dn.net/?f=%5Cfrac%7B%282%5E%7B5%2A%5Cfrac%7B1%7D%7B3%7D%7Dx%2Ay%5E%7B2%7D%29%7D%7B%282%5E%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%7D%2Ay%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%7D)
![\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}](https://tex.z-dn.net/?f=%5Cfrac%7B%282%5E%7B%5Cfrac%7B5%7D%7B3%7D%7Dx%2Ay%5E%7B2%7D%29%7D%7B%282%5E%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%7D%2Ay%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%7D)
From laws of indices
![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
This law can be applied to the expression above;
becomes
![2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B5%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7Dx%5E%7B1-3%7D%2Ay%5E%7B2-%5Cfrac%7B2%7D%7B3%7D%7D)
Solve exponents
![2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B5-1%7D%7B3%7D%7D%2Ax%5E%7B-2%7D%2Ay%5E%7B%5Cfrac%7B6-2%7D%7B3%7D%7D)
![2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%2Ax%5E%7B-2%7D%2Ay%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D)
From laws of indices,
; So,
gives
![\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%2Ay%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%7D%7Bx%5E2%7D)
The expression at the numerator can be combined to give
![\frac{(2y)^{\frac{4}{3}}}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%282y%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%7D%7Bx%5E2%7D)
Lastly, From laws of indices,
; So,
becomes
![\frac{\sqrt[3]{(2y)}^{4}}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B%282y%29%7D%5E%7B4%7D%7D%7Bx%5E2%7D)
![\frac{\sqrt[3]{16y^4}}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B16y%5E4%7D%7D%7Bx%5E2%7D)
Hence,
is equivalent to ![\frac{\sqrt[3]{16y^4}}{x^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B16y%5E4%7D%7D%7Bx%5E2%7D)