The fastest way is to just use a scientific calculator.
To do it without a calculator, use prime factorization.
I'll only do the second one which is the answer.
27 x 8
= 3^3 x 2^3 = 6^3
Which is a perfect cube.
Answer:
6
Step-by-step explanation:
We want to expand this; (x + y)⁴
This can be written as;
(x + y)² × (x + y)²
This gives;
(x² + 2xy + y²) × (x² + 2xy + y²)
This gives;
x²(x² + 2xy + y²) + 2xy(x² + 2xy + y²) + y²(x² + 2xy + y²) = x⁴ + 2x³y + x²y² + 2x³y + 4x²y² + 2xy³ + x²y² + 2xy³ + y⁴
Simplifying gives;
x⁴ + 4x³y + 4xy³ + 6x²y² + y⁴
Thus, the coefficient of x²y² is 6
9514 1404 393
Answer:
a.
Step-by-step explanation:
For an even-index radical, ...
![\sqrt[n]{x^n}=|x|\qquad\text{n even}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5En%7D%3D%7Cx%7C%5Cqquad%5Ctext%7Bn%20even%7D)
This lets us simplify the given expression as follows:
![\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81x%5E6y%5E4%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E6%7D-%5Csqrt%5B4%5D%7B16x%5E2%7D%3D%5Csqrt%5B4%5D%7B%283xy%29%5E4x%5E2%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E4x%5E2%7D-%5Csqrt%5B4%5D%7B2%5E4x%5E2%7D%5C%5C%5C%5C%3D3%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%3D%5Cboxed%7B2%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%7D)
Answer:
x<27
Step-by-step explanation:
2(x+x+4)<116
2(2x+4)<116
2x+4<58
2x<54
x<27
