Solve operatorname{tm}(4m^2p)^2div7m^2

$$\operatorname { tm } ( 4 m ^ { 2 } p ) ^ { 2 } \div 7 m ^ { 2 }$$

Evaluate

$$\frac{16tp^{2}m^{7}}{7}$$

Solution Steps

Expand \left(4m^{2}p\right)^{2}.

$$\frac{tm\times 4^{2}\left(m^{2}\right)^{2}p^{2}}{7}m^{2}$$

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

$$\frac{tm\times 4^{2}m^{4}p^{2}}{7}m^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{tm\times 16m^{4}p^{2}}{7}m^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{tm^{5}\times 16p^{2}}{7}m^{2}$$

Express \frac{tm^{5}\times 16p^{2}}{7}m^{2} as a single fraction.

$$\frac{tm^{5}\times 16p^{2}m^{2}}{7}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{tm^{7}\times 16p^{2}}{7}$$

Expand

$$\frac{16tp^{2}m^{7}}{7}$$

Solution Steps

Expand \left(4m^{2}p\right)^{2}.

$$\frac{tm\times 4^{2}\left(m^{2}\right)^{2}p^{2}}{7}m^{2}$$

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

$$\frac{tm\times 4^{2}m^{4}p^{2}}{7}m^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{tm\times 16m^{4}p^{2}}{7}m^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{tm^{5}\times 16p^{2}}{7}m^{2}$$

Express \frac{tm^{5}\times 16p^{2}}{7}m^{2} as a single fraction.

$$\frac{tm^{5}\times 16p^{2}m^{2}}{7}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{tm^{7}\times 16p^{2}}{7}$$