Solve 4t^8*(4t^2)^2/4t^4

$$\frac { 4 t ^ { 8 } \times ( 4 t ^ { 2 } ) ^ { 2 } } { 4 t ^ { 4 } }$$

Evaluate

$$16t^{8}$$

Solution Steps

Cancel out 4t^{4} in both numerator and denominator.

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

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

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

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

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

Calculate 4 to the power of 2 and get 16.

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$t^{8}\times 16$$

Expand

$$16t^{8}$$

Solution Steps

Cancel out 4t^{4} in both numerator and denominator.

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

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

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

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

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

Calculate 4 to the power of 2 and get 16.

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$t^{8}\times 16$$