Solve A=314(2p^5)^2

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

Solve for A

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 314 and 4 to get 1256.

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

Solve for p

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

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