Penjelasan langkah demi langkah:
1)
![= 243^{\frac{2}{3} }\\= (\sqrt[3]{243})^2\\= 7^2\\= 49](https://tex.z-dn.net/?f=%3D%20243%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D%5C%5C%3D%20%28%5Csqrt%5B3%5D%7B243%7D%29%5E2%5C%5C%3D%207%5E2%5C%5C%3D%2049)
2) √32 +3√18-2√50
= √16*2 +3√9*2-2√25*2
= 4√2 + 3(3√2)-2(5√2)
= 4√2 + 9√2-10√2
= 13√2-10√2
= 3√2
3) 1000 ⅔×64⅙
![= (\sqrt[3]{1000}) ^2 \times (2^6)^{1/6} \\= 10^2 \times 2\\= 100 \times 2\\= 200](https://tex.z-dn.net/?f=%3D%20%28%5Csqrt%5B3%5D%7B1000%7D%29%20%5E2%20%5Ctimes%20%282%5E6%29%5E%7B1%2F6%7D%20%20%5C%5C%3D%2010%5E2%20%5Ctimes%202%5C%5C%3D%20100%20%5Ctimes%202%5C%5C%3D%20200)
4) 3/4+√2

5) 2√3×√18
= 2√3×√9*2
= 2√3×3√2
= (2*3)(√3*√2)
= 6√6
6) 12/3+√3
= 4+√3
7) √1000—2√40
= 10 -2 (√4*10)
= 10-2(2√10)
= 10 - 4√10
8) 2- ¹+3-¹

9)

Jika pernyataannya opsional, penyebutnya adalah 1
10) 2√3×√18
= 2√3×√9*2
= 2√3×3√2
= (2*3)(√3*√2)
= 6√6
Answer:

Four raised to the one-sixth power
Step-by-step explanation:
We want to simplify: ![\dfrac{\sqrt{4} }{\sqrt[3]{4} }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B4%7D%20%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D)
First, we apply the fractional law of indices to each term.
![\text{If } a^{1/x}=\sqrt[x]{a},$ then:\\\sqrt{4}=4^{1/2}\\\sqrt[3]{4}=4^{1/3}](https://tex.z-dn.net/?f=%5Ctext%7BIf%20%20%7D%20a%5E%7B1%2Fx%7D%3D%5Csqrt%5Bx%5D%7Ba%7D%2C%24%20then%3A%5C%5C%5Csqrt%7B4%7D%3D4%5E%7B1%2F2%7D%5C%5C%5Csqrt%5B3%5D%7B4%7D%3D4%5E%7B1%2F3%7D)
We then have:
![\dfrac{\sqrt{4} }{\sqrt[3]{4} }=\dfrac{4^{1/2} }{4^{1/3} }\\$Applying the division law of indices: \dfrac{a^m }{a^n }=a^{m-n}\\\dfrac{4^{1/2} }{4^{1/3} }=4^{1/2-1/3}\\\\=4^{1/6}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B4%7D%20%7D%7B%5Csqrt%5B3%5D%7B4%7D%20%7D%3D%5Cdfrac%7B4%5E%7B1%2F2%7D%20%7D%7B4%5E%7B1%2F3%7D%20%7D%5C%5C%24Applying%20the%20division%20law%20of%20indices%3A%20%5Cdfrac%7Ba%5Em%20%7D%7Ba%5En%20%7D%3Da%5E%7Bm-n%7D%5C%5C%5Cdfrac%7B4%5E%7B1%2F2%7D%20%7D%7B4%5E%7B1%2F3%7D%20%7D%3D4%5E%7B1%2F2-1%2F3%7D%5C%5C%5C%5C%3D4%5E%7B1%2F6%7D)
The correct option is B.
Answer: a. The unit for the numerator is Dollars
b. The unit for the denominator is seconds.
Answer:
p=7x
Step-by-step explanation:
49x^[2] + 28x - 10 = p^[2] + 4p -10
This equation is in the form a^[2]x + bx + c.
<u><em>The 'c' is common for both equations, this means the 'a' and 'b' must also be common. </em></u>
There are two ways to find p: 'a' or 'b'
<u>a method</u>
49x^[2] = p^[2]
=> The square root of both sides = 7x = p
<u>b method</u>
28x = 4p
28x/4 = 4p/4
7x = p