Solve (5k^{2}m)^3[(4km^4)^2]^2

$$( 5 k ^ { 2 } m ) ^ { 3 } [ ( 4 k m ^ { 4 } ) ^ { 2 } ] ^ { 2 }$$

Evaluate

$$32000k^{10}m^{19}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(5k^{2}m\right)^{3}\times \left(4km^{4}\right)^{4}$$

Expand \left(5k^{2}m\right)^{3}.

$$5^{3}\left(k^{2}\right)^{3}m^{3}\times \left(4km^{4}\right)^{4}$$

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

$$5^{3}k^{6}m^{3}\times \left(4km^{4}\right)^{4}$$

Calculate 5 to the power of 3 and get 125.

$$125k^{6}m^{3}\times \left(4km^{4}\right)^{4}$$

Expand \left(4km^{4}\right)^{4}.

$$125k^{6}m^{3}\times 4^{4}k^{4}\left(m^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$125k^{6}m^{3}\times 4^{4}k^{4}m^{16}$$

Calculate 4 to the power of 4 and get 256.

$$125k^{6}m^{3}\times 256k^{4}m^{16}$$

Multiply 125 and 256 to get 32000.

$$32000k^{6}m^{3}k^{4}m^{16}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$32000k^{10}m^{3}m^{16}$$

To multiply powers of the same base, add their exponents. Add 3 and 16 to get 19.

$$32000k^{10}m^{19}$$

Expand

$$32000k^{10}m^{19}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(5k^{2}m\right)^{3}\times \left(4km^{4}\right)^{4}$$

Expand \left(5k^{2}m\right)^{3}.

$$5^{3}\left(k^{2}\right)^{3}m^{3}\times \left(4km^{4}\right)^{4}$$

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

$$5^{3}k^{6}m^{3}\times \left(4km^{4}\right)^{4}$$

Calculate 5 to the power of 3 and get 125.

$$125k^{6}m^{3}\times \left(4km^{4}\right)^{4}$$

Expand \left(4km^{4}\right)^{4}.

$$125k^{6}m^{3}\times 4^{4}k^{4}\left(m^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$125k^{6}m^{3}\times 4^{4}k^{4}m^{16}$$

Calculate 4 to the power of 4 and get 256.

$$125k^{6}m^{3}\times 256k^{4}m^{16}$$

Multiply 125 and 256 to get 32000.

$$32000k^{6}m^{3}k^{4}m^{16}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$32000k^{10}m^{3}m^{16}$$

To multiply powers of the same base, add their exponents. Add 3 and 16 to get 19.

$$32000k^{10}m^{19}$$