Lahenda [(15div5)^{4}]^{3}:[(2^{2}*5*3):12*2^5:2^4]^10-1^3

$$[ ( 15 \div 5 ) ^ { 4 } ] ^ { 3 } : [ ( 2 ^ { 2 } \times 5 \times 3 ) : 12 \cdot 2 ^ { 5 } : 2 ^ { 4 } ] ^ { 10 } - 1 ^ { 3 }$$

Arvuta

$$-\frac{9999468559}{10000000000}\approx -0,999946856$$

Lahenduse etapid

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 4 ja 3, et saada 12.

$$\frac{\left(\frac{15}{5}\right)^{12}}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Jagage 15 väärtusega 5, et leida 3.

$$\frac{3^{12}}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Arvutage 12 aste 3 ja leidke 531441.

$$\frac{531441}{\left(\frac{\frac{2^{2}\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Arvutage 2 aste 2 ja leidke 4.

$$\frac{531441}{\left(\frac{\frac{4\times 5\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Korrutage 4 ja 5, et leida 20.

$$\frac{531441}{\left(\frac{\frac{20\times 3}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Korrutage 20 ja 3, et leida 60.

$$\frac{531441}{\left(\frac{\frac{60}{12}\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Jagage 60 väärtusega 12, et leida 5.

$$\frac{531441}{\left(\frac{5\times 2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

Arvutage 5 aste 2 ja leidke 32.

$$\frac{531441}{\left(\frac{5\times 32}{2^{4}}\right)^{10}}-1^{3}$$

Korrutage 5 ja 32, et leida 160.

$$\frac{531441}{\left(\frac{160}{2^{4}}\right)^{10}}-1^{3}$$

Arvutage 4 aste 2 ja leidke 16.

$$\frac{531441}{\left(\frac{160}{16}\right)^{10}}-1^{3}$$

Jagage 160 väärtusega 16, et leida 10.

$$\frac{531441}{10^{10}}-1^{3}$$

Arvutage 10 aste 10 ja leidke 10000000000.

$$\frac{531441}{10000000000}-1^{3}$$

Arvutage 3 aste 1 ja leidke 1.

$$\frac{531441}{10000000000}-1$$

Lahutage 1 väärtusest \frac{531441}{10000000000}, et leida -\frac{9999468559}{10000000000}.

$$-\frac{9999468559}{10000000000}$$

Lahuta teguriteks

$$-\frac{9999468559}{10000000000} = -0,9999468559$$