Question

1, Tìm x

a, (3x^2-50)^2=5^4

2, Rút gọn

a, (3^4-3^3)^4/27^3

b, 25^3/(5^5-5^3)^2

3, Thực hiện phép tính

a, (-1/3)^2 . 9 - (1/2)^3 .16 +(2:1/2^2)

b, (3/7)^10 . (7^5)^9 : (9/25)^5

c, (0,25)^5 . 2^11 : (1/3)^2

Answer 1

1)

a. \(\left(3x^2-50\right)^2=5^4\)

\(\Leftrightarrow3x^4-50=625\)

\(\Leftrightarrow3x^4=675\)

\(\Leftrightarrow x^4=225\)

\(\Leftrightarrow x=\sqrt{15}\) 

2)

a. \(\frac{\left(3^4-3^3\right)^4}{27^3}=\frac{3^{16}-3^{12}}{\left(3^3\right)^3}=\frac{3^{12}.3^4-3^{12}}{3^9}=\frac{3^{12}\left(3^4-1\right)}{3^9}\)

\(=\frac{3^{12}.80}{3^9}=3^3.80=27.80=2160\)

b. \(\frac{25^3}{\left(5^5-5^3\right)^2}=\frac{\left(5^2\right)^3}{5^{10}-5^6}=\frac{5^6}{5^6.5^4-5^6}=\frac{5^6}{5^6\left(5^4-1\right)}\)

\(=\frac{5^6}{5^6.624}=\frac{1}{624}\)