\(125\cdot30+250\cdot33+125\cdot4\\ =125\cdot30+125\cdot\left(2\cdot33\right)+125\cdot4\\ =125\cdot30+125\cdot66+125\cdot4\\ =125\cdot\left(30+66+4\right)\\ =125\cdot100\\ =12500\)

\(\left(x-3\right)^6=\left(x-3\right)^4\\ \Leftrightarrow\left(x-3\right)^6:\left(x-3\right)^4=\left(x-3\right)^4:\left(x-3\right)^4\\ \Leftrightarrow\left(x-3\right)^2=\left(x-3\right)^0\\ \Leftrightarrow\left(x-3\right)^2=1\\ \Leftrightarrow\left(x-3\right)^2=1^2\\ \Leftrightarrow x-3=1\\ \Leftrightarrow x=1+3=4\)

Vậy \(x=4\) thỏa mãn bài toán.

5 x (5 - 5 + 5) : 5 = 5

Ta có: \(\dfrac{x}{4}=\dfrac{y}{3}\) và \(xy=12\)

\(\Leftrightarrow3x=4y\)

\(\Leftrightarrow x=\dfrac{4}{3}y\)

\(\Rightarrow xy=\dfrac{4}{3}y\cdot y=12\)

\(\Leftrightarrow y\cdot y=12:\dfrac{4}{3}\)

\(\Leftrightarrow y^2=12\cdot\dfrac{3}{4}\)

\(\Leftrightarrow y^2=9\)

\(\Leftrightarrow y^2=3^2\)

\(\Leftrightarrow y=3\)

\(\Rightarrow x=12:y=12:3=4\)

Vậy x = 4 và y = 3.

\(2^{x-2}=64\)

\(\Leftrightarrow2^{x-2}=2^6\)

\(\Leftrightarrow x-2=6\)

\(\Leftrightarrow x=6+2\)

\(\Leftrightarrow x=8\)

Vậy \(x=8\).

\(x^2-4=0\)

\(\Leftrightarrow x^2=0+4\)

\(\Leftrightarrow x^2=4\)

\(\Leftrightarrow x^2=2^2\) hoặc \(x^2=\left(-2\right)^2\)

\(\Leftrightarrow x=2\) hoặc \(x=-2\)

Vậy \(x=2\) hoặc \(x=-2\).

free/ He/ most/ time/ sports/ spends/ of/ his/ playing/.

==> He spends his most of free time playing sports.

\(5^{40}\cdot125^2\cdot625^3\)

\(=5^{40}\cdot\left(5^2\cdot5^2\cdot5^2\right)\cdot\left(5^3\cdot5^3\cdot5^3\cdot5^3\right)\)

\(=5^{40}\cdot5^6\cdot5^{12}\)

\(=5^{46}\cdot5^{12}\)

\(=5^{58}\)

Vậy \(5^{40}\cdot125^2\cdot625^3=5^{58}\).