Answer:
![\sqrt{63}\times \sqrt[3]{56}\times7^{\frac{1}{6}}=42](https://tex.z-dn.net/?f=%5Csqrt%7B63%7D%5Ctimes%20%5Csqrt%5B3%5D%7B56%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%3D42)
Step-by-step explanation:
Given : Expression ![\sqrt{63}\times \sqrt[3]{56}\times7^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Csqrt%7B63%7D%5Ctimes%20%5Csqrt%5B3%5D%7B56%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
To find : What is the value of the expression ?
Solution :
Step 1 - Write the expression as
![(63)^{\frac{1}{2}}\times(56)^{\frac{1}{3}}\times7^{\frac{1}{6}}](https://tex.z-dn.net/?f=%2863%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes%2856%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Step 2 - Factor 63 and 56 as multiple of 7,
![(7\times 9)^{\frac{1}{2}}\times(7\times 8)^{\frac{1}{3}}\times7^{\frac{1}{6}}](https://tex.z-dn.net/?f=%287%5Ctimes%209%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes%287%5Ctimes%208%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Step 3 - Split the powers ![(a\times b)^c=a^c\times b^c](https://tex.z-dn.net/?f=%28a%5Ctimes%20b%29%5Ec%3Da%5Ec%5Ctimes%20b%5Ec)
![7^{\frac{1}{2}}\times 9^{\frac{1}{2}}\times7^{\frac{1}{3}}\times 8^{\frac{1}{3}}\times7^{\frac{1}{6}}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes%209%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%208%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Step 4 - Add the same base power, ![a^b\times a^c=a^{b+c}](https://tex.z-dn.net/?f=a%5Eb%5Ctimes%20a%5Ec%3Da%5E%7Bb%2Bc%7D)
![=7^{\frac{1}{2}+\frac{1}{3}+\frac{1}{6}}\times (3^2)^{\frac{1}{2}}\times (2^3)^{\frac{1}{3}}](https://tex.z-dn.net/?f=%3D7%5E%7B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B6%7D%7D%5Ctimes%20%283%5E2%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctimes%20%282%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![=7^{\frac{3+2+1}{6}}\times (3)^{\frac{2}{2}}\times (2)^{\frac{3}{3}}](https://tex.z-dn.net/?f=%3D7%5E%7B%5Cfrac%7B3%2B2%2B1%7D%7B6%7D%7D%5Ctimes%20%283%29%5E%7B%5Cfrac%7B2%7D%7B2%7D%7D%5Ctimes%20%282%29%5E%7B%5Cfrac%7B3%7D%7B3%7D%7D)
![=7^{\frac{6}{6}}\times (3)^{1}\times (2)^{1}](https://tex.z-dn.net/?f=%3D7%5E%7B%5Cfrac%7B6%7D%7B6%7D%7D%5Ctimes%20%283%29%5E%7B1%7D%5Ctimes%20%282%29%5E%7B1%7D)
![=7\times3\times2](https://tex.z-dn.net/?f=%3D7%5Ctimes3%5Ctimes2)
![=42](https://tex.z-dn.net/?f=%3D42)
Therefore, ![\sqrt{63}\times \sqrt[3]{56}\times7^{\frac{1}{6}}=42](https://tex.z-dn.net/?f=%5Csqrt%7B63%7D%5Ctimes%20%5Csqrt%5B3%5D%7B56%7D%5Ctimes7%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%3D42)
35. 20+15=30. 2 tens=20+15 hope this helps!
(-2m + 5n)²
(-2m + 5n) (-2m + 5n)
-2m(-2m + 5n) + 5n(-2m + 5n)
4m² - 10mn - 10mn + 25n²
4m² - 20mn + 25n²
4m²⇒ -2m * -2m
-20mn ⇒ 2(-2m)(5n)
25n² ⇒ 5n * 5n
<span>C. 4m² − 20mn + 25n²; a perfect square trinomial</span>
Answer:more than half so it should be 42
Step-by-step explanation:
Answer:
x= i√2, -i√2
Step-by-step explanation: