2 replies to this topic

[lemai03]

1. Tính 

    a) $\frac{49^{5}.7^{16}}{7^{18}.7^{6}}$

    b) $\frac{4^{16}.8^{20}}{2^{14}.32^{15}}$

2. Tìm $x$

    a) $\left ( \frac{3}{2}. x +\frac{4}{3} \right )^{2}=\frac{4}{9}$

    b) $\left ( \frac{7}{15}-\frac{3}{20}.x \right )^{3}=\frac{-8}{125}$

3. Rút gọn

    a) $x ^{n+1}.x ^{n+2}$

    b) $x ^{3.( n+4)}\div x^{2( n-1)}$

Edited by votruc, 14-07-2015 - 10:29.

[hoctrocuaHolmes]

1. Tính 

    a) $\frac{49^{5}.7^{16}}{7^{18}.7^{6}}$

    b) $\frac{4^{16}.8^{20}}{2^{14}.32^{15}}$

2. Tìm $x$

    a) $\left ( \frac{3}{2}. x +\frac{4}{3} \right )^{2}=\frac{4}{9}$

    b) $\left ( \frac{7}{15}-\frac{3}{20}.x \right )^{3}=\frac{-8}{125}$

3. Rút gọn

    a) $x ^{n+1}.x ^{n+2}$

    b) $x ^{3.( n+4)}\div x^{2( n-1)}$

1.a) $\frac{49^{5}.7^{16}}{7^{18}.7^{6}}=\frac{(7^{2})^{5}.7^{16}}{7^{18+6}}=\frac{7^{10+16}}{7^{24}}=\frac{7^{26}}{7^{24}}=7^{2}$

b)$\frac{4^{16}.8^{20}}{2^{14}.32^{15}}=\frac{(2^{2})^{16}.(2^{3})^{20}}{2^{14}.(2^{5})^{15}}=\frac{2^{32+60}}{2^{14+75}}=2^{3}$

2.a)$\left ( \frac{3}{2}. x +\frac{4}{3} \right )^{2}=\frac{4}{9}$

$\Leftrightarrow \begin{bmatrix} \frac{3}{2}x=\frac{-2}{3} & \\ \frac{3}{2}x=-2 & \end{bmatrix}\Leftrightarrow \begin{bmatrix} x=\frac{-4}{9} & \\ x=\frac{-4}{3} & \end{bmatrix}$

b)$\left ( \frac{7}{15}-\frac{3}{20}x \right )^{3}=\frac{-8}{125}$

$\Leftrightarrow \frac{7}{15}-\frac{3}{20}x=\frac{-2}{5}$

$\Leftrightarrow \frac{3}{20}x=\frac{13}{15}\Leftrightarrow x=\frac{260}{45}$

Edited by votruc, 14-07-2015 - 10:47.

[hoctrocuaHolmes]

3. Rút gọn    a) $x ^{n+1}.x ^{n+2}$

    b) $x ^{3.( n+4)}\div x^{2( n-1)}$

3.a)$x ^{n+1}.x ^{n+2}=x^{n+1+n+2}=x^{2n+3}$

b)$x ^{3.( n+4)}\div x^{2( n-1)}=x^{3(n+4)-2(n-1)}=x^{3n+12-2n+2}=x^{n+14}$