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

Also from laws of indices

So, the above expression can be further simplified to

Multiply the exponents gives

Substitute
for 32


From laws of indices

This law can be applied to the expression above;
becomes

Solve exponents


From laws of indices,
; So,
gives

The expression at the numerator can be combined to give

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)
I think that u might want to do the share the company money i could be wrong but if i sm sorry
Answer:
Step-by-step explanation:
5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.
Answer:
<em>Mrs. Adams will earn $3,120 of interest at the end of year 8.</em>
Step-by-step explanation:
<u>Simple Interest</u>
In simple interest, the money earns interest at a fixed rate, assuming no new money is coming in or out of the account.
We can calculate the interests earned by an investment of value A in a period of time t, at an interest rate r with the formula:

Mrs. Adams deposited an amount of A=$12,000 into an account that earns an annual simple interest rate of r=3.25%. We must find the interest earned in t=8 years. The interest rate is converted to decimal as:

The interest is then calculated:

Mrs. Adams will earn $3,120 of interest at the end of year 8.
Set up a proportion with Katie’s height / Katie’s shadow = roller coasters height / its shadow. So it is 5 feet / 2 feet = x feet / 60 feet. To solve cross multiply so it becomes 2x = 300 and x = 150 feet