Løs A=314(2p^5)^2

$$A = 314 ( 2 p ^ { 5 } ) ^ { 2 }$$

Løs for A

$$A=1256p^{10}$$

Løsningstrinn

Utvid \left(2p^{5}\right)^{2}.

$$A=314\times 2^{2}\left(p^{5}\right)^{2}$$

Hvis du vil opphøye potensen til et tall til en annen potens, multipliserer du eksponentene. Multipliser 5 og 2 for å få 10.

$$A=314\times 2^{2}p^{10}$$

Regn ut 2 opphøyd i 2 og få 4.

$$A=314\times 4p^{10}$$

Multipliser 314 med 4 for å få 1256.

$$A=1256p^{10}$$

Løs for p (complex solution)

$$p\in \frac{1256^{\frac{9}{10}}e^{\frac{\pi i}{5}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{2\pi i}{5}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{3\pi i}{5}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{4\pi i}{5}}\sqrt[10]{A}}{1256},-\frac{1256^{\frac{9}{10}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{6\pi i}{5}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{7\pi i}{5}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{8\pi i}{5}}\sqrt[10]{A}}{1256},\frac{1256^{\frac{9}{10}}e^{\frac{9\pi i}{5}}\sqrt[10]{A}}{1256}$$

Løs for p

$$p=\frac{1256^{\frac{9}{10}}\sqrt[10]{A}}{1256}$$

$$p=-\frac{1256^{\frac{9}{10}}\sqrt[10]{A}}{1256}\text{, }A\geq 0$$