Solve 4p^2*(2p^3)^2

$$4 p ^ { 2 } \cdot ( 2 p ^ { 3 } ) ^ { 2 }$$

Evaluate

$$16p^{8}$$

Solution Steps

Expand \left(2p^{3}\right)^{2}.

$$4p^{2}\times 2^{2}\left(p^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$4p^{2}\times 2^{2}p^{6}$$

Calculate 2 to the power of 2 and get 4.

$$4p^{2}\times 4p^{6}$$

Multiply 4 and 4 to get 16.

$$16p^{2}p^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$16p^{8}$$

Expand

$$16p^{8}$$

Solution Steps

Expand \left(2p^{3}\right)^{2}.

$$4p^{2}\times 2^{2}\left(p^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$4p^{2}\times 2^{2}p^{6}$$

Calculate 2 to the power of 2 and get 4.

$$4p^{2}\times 4p^{6}$$

Multiply 4 and 4 to get 16.

$$16p^{2}p^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$16p^{8}$$