Issolvi [(-2/5)^{2}*(1/4)^{2}]^{2}:(5^{2}*2^{2})^-2-(4/5)^-5*(-4/5)^-4:(frac{4}{5})^-7

$$[ ( - \frac { 2 } { 5 } ) ^ { 2 } \cdot ( \frac { 1 } { 4 } ) ^ { 2 } ] ^ { 2 } : ( 5 ^ { 2 } \cdot 2 ^ { 2 } ) ^ { - 2 } - ( \frac { 4 } { 5 } ) ^ { - 5 } \cdot ( - \frac { 4 } { 5 } ) ^ { - 4 } : ( \frac { 4 } { 5 } ) ^ { - 7 }$$

Evalwa

$$-\frac{9}{16}=-0.5625$$

Passi tas-Soluzzjonijiet

Ikkalkula -\frac{2}{5} bil-power ta' 2 u tikseb \frac{4}{25}.

$$\frac{\left(\frac{4}{25}\times \left(\frac{1}{4}\right)^{2}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Ikkalkula \frac{1}{4} bil-power ta' 2 u tikseb \frac{1}{16}.

$$\frac{\left(\frac{4}{25}\times \frac{1}{16}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Immultiplika \frac{4}{25} u \frac{1}{16} biex tikseb \frac{1}{100}.

$$\frac{\left(\frac{1}{100}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Ikkalkula \frac{1}{100} bil-power ta' 2 u tikseb \frac{1}{10000}.

$$\frac{\frac{1}{10000}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

$$\frac{\frac{1}{10000}}{\left(25\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{\frac{1}{10000}}{\left(25\times 4\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Immultiplika 25 u 4 biex tikseb 100.

$$\frac{\frac{1}{10000}}{100^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Ikkalkula 100 bil-power ta' -2 u tikseb \frac{1}{10000}.

$$\frac{\frac{1}{10000}}{\frac{1}{10000}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Iddividi \frac{1}{10000} b'\frac{1}{10000} biex tikseb1.

$$1-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur.

$$1-\left(-\frac{4}{5}\right)^{-4}\times \left(\frac{4}{5}\right)^{2}$$

Ikkalkula -\frac{4}{5} bil-power ta' -4 u tikseb \frac{625}{256}.

$$1-\frac{625}{256}\times \left(\frac{4}{5}\right)^{2}$$

Ikkalkula \frac{4}{5} bil-power ta' 2 u tikseb \frac{16}{25}.

$$1-\frac{625}{256}\times \frac{16}{25}$$

Immultiplika \frac{625}{256} u \frac{16}{25} biex tikseb \frac{25}{16}.

$$1-\frac{25}{16}$$

Naqqas \frac{25}{16} minn 1 biex tikseb -\frac{9}{16}.

$$-\frac{9}{16}$$

Fattur

$$-\frac{9}{16} = -0.5625$$