Solve (s^{-2}t^2)^2(8^2t^3)

$$( s ^ { - 2 } t ^ { 2 } ) ^ { 2 } ( 8 ^ { 2 } t ^ { 3 } )$$

Evaluate

$$\frac{64t^{7}}{s^{4}}$$

Solution Steps

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

$$\left(s^{-2}\right)^{2}\left(t^{2}\right)^{2}\times 8^{2}t^{3}$$

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

$$s^{-4}\left(t^{2}\right)^{2}\times 8^{2}t^{3}$$

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

$$s^{-4}t^{4}\times 8^{2}t^{3}$$

Calculate 8 to the power of 2 and get 64.

$$s^{-4}t^{4}\times 64t^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$s^{-4}t^{7}\times 64$$

Expand

$$\frac{64t^{7}}{s^{4}}$$

Solution Steps

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

$$\left(s^{-2}\right)^{2}\left(t^{2}\right)^{2}\times 8^{2}t^{3}$$

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

$$s^{-4}\left(t^{2}\right)^{2}\times 8^{2}t^{3}$$

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

$$s^{-4}t^{4}\times 8^{2}t^{3}$$

Calculate 8 to the power of 2 and get 64.

$$s^{-4}t^{4}\times 64t^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$s^{-4}t^{7}\times 64$$