Question

1- (1/2×3/5×2/3)²=?
2- (4/7)⁴÷(4/7)²=?
AYUDAAAAAAA PORFA ​

Answer 1

Respuesta:

$\left(\frac{1}{2}\times \frac{3}{5}\times \frac{2}{3}\right)^2=\frac{1}{25}$

$\frac{\left(\frac{4}{7}\right)^4}{\left(\frac{4}{7}\right)^2}=\frac{16}{49}$

Explicación paso a paso:

$\left(\frac{1}{2}\times \frac{3}{5}\times \frac{2}{3}\right)^2$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a\times \:b\right)^n=a^nb^n$

$\left(\frac{1}{2}\times \frac{3}{5}\times \frac{2}{3}\right)^2=\left(\frac{1}{2}\right)^2\left(\frac{3}{5}\right)^2\left(\frac{2}{3}\right)^2$

$\left(\frac{1}{2}\right)^2=\frac{1}{4}$

$\left(\frac{3}{5}\right)^2=\frac{9}{25}$

$\left(\frac{2}{3}\right)^2=\frac{4}{9}$

$=\frac{1}{4}\times \frac{9}{25}\times \frac{4}{9}$

$=\frac{1\times \:9\times \:4}{4\times \:25\times \:9}$

$\mathrm{Eliminar\:los\:terminos\:comunes:}$

$=\frac{1}{25}$

$\frac{\left(\frac{4}{7}\right)^4}{\left(\frac{4}{7}\right)^2}$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \frac{x^a}{x^b}=x^{a-b}$

$=\left(\frac{4}{7}\right)^{4-2}$

$=\left(\frac{4}{7}\right)^2$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{4^2}{7^2}$

$=\frac{16}{49}$

Buen día