tớ nghĩ cùng mũ nhân tử : \(2^7.5^7=\left(2.5\right)^7=10^7\)

\(2^7.5^7=\left(2.5\right)^7=10^7\)

( 2. 5 )⁷ = 10⁷

13.

$(x+4)^2+(x+5)(x-5)-2x(x+1)$

$=(x^2+8x+16)+(x^2-25)-(2x^2+2x)$

$=x^2+8x+16+x^2-25-2x^2-2x$

$=(x^2+x^2-2x^2)+(8x-2x)+(16-25)=6x-9$

14.

$(x-1)^2-2(x+3)(x-3)+4x(x-4)$

$=(x^2-2x+1)-2(x^2-9)+(4x^2-16x)$

$=x^2-2x+1-2x^2+18+4x^2-16x$

$=(x^2-2x^2+4x^2)+(-2x-16x)+(1+18)=3x^2-18x+19$

15.

$(y-3)(y+3)(y^2+9)-(y^2+2)(y^2-2)$

$=(y^2-9)(y^2+9)-(y^4-4)$

$=(y^4-81)-(y^4-4)=-81+4=-77$

Câu 1: 4¹⁴ . 5²⁸ = 4¹⁴ . (5²)¹⁴ = 4¹⁴ . 25¹⁴ = (4.25)¹⁴ = 100¹⁴

Câu 2: 12⁸ . 2¹⁶ = 12⁸ . (2²)⁸ = 12⁸ . 4⁸ = (12.4)⁸ = 48⁸

ĐKXĐ:

\(\left\{{}\begin{matrix}x\ge0\\1-x\ne0\\1+x\sqrt{x}\ne0\\2\sqrt{x}-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne1\\x\ne\dfrac{1}{4}\end{matrix}\right.\)

\(A=1-\left(\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right)\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)

\(A=1-\left(\dfrac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{\left(1+\sqrt{x}\right)\left(x-\sqrt{x}+1\right)}\right)\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)

\(A=1-\left(\dfrac{1}{1-\sqrt{x}}+\dfrac{\sqrt{x}}{1-\sqrt{x}+x}\right)\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)\)

\(A=1-\dfrac{1-\sqrt{x}+x+\sqrt{x}-x}{\left(1-\sqrt{x}\right)\left(1-\sqrt{x}+x\right)}\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)\)

\(A=1-\dfrac{x-\sqrt{x}}{1-\sqrt{x}+x}=\dfrac{1-\sqrt{x}+x-x+\sqrt{x}}{1-\sqrt{x}+x}=\dfrac{1}{1-\sqrt{x}+x}\)

`2424/4545=(2424:303)/(4545:303)=8/15`

= 8/15 

Nhớ tick nha