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

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

Evaluate

$$256p^{9}$$

Solution Steps

Expand \left(4p\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

$$64p^{3}\times \left(2p\right)^{2}p^{4}$$

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

$$64p^{3}\times 2^{2}p^{2}p^{4}$$

Calculate 2 to the power of 2 and get 4.

$$64p^{3}\times 4p^{2}p^{4}$$

Multiply 64 and 4 to get 256.

$$256p^{3}p^{2}p^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$256p^{5}p^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$256p^{9}$$

Expand

$$256p^{9}$$

Solution Steps

Expand \left(4p\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

$$64p^{3}\times \left(2p\right)^{2}p^{4}$$

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

$$64p^{3}\times 2^{2}p^{2}p^{4}$$

Calculate 2 to the power of 2 and get 4.

$$64p^{3}\times 4p^{2}p^{4}$$

Multiply 64 and 4 to get 256.

$$256p^{3}p^{2}p^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$256p^{5}p^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$256p^{9}$$