Solve 12t^5*(4t^2)^2/12t^3

$$\frac { 12 t ^ { 5 } \times ( 4 t ^ { 2 } ) ^ { 2 } } { 12 t ^ { 3 } }$$

Evaluate

$$16t^{6}$$

Solution Steps

Cancel out 12t^{3} in both numerator and denominator.

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

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

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

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

$$t^{2}\times 4^{2}t^{4}$$

Calculate 4 to the power of 2 and get 16.

$$t^{2}\times 16t^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$t^{6}\times 16$$

Expand

$$16t^{6}$$

Solution Steps

Cancel out 12t^{3} in both numerator and denominator.

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

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

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

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

$$t^{2}\times 4^{2}t^{4}$$

Calculate 4 to the power of 2 and get 16.

$$t^{2}\times 16t^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$t^{6}\times 16$$