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

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

Evaluate

$$\frac{t^{7}}{s^{2}}$$

Solution Steps

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

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

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

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

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

$$s^{-4}t^{4}s^{2}t^{3}$$

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

$$s^{-2}t^{4}t^{3}$$

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

$$s^{-2}t^{7}$$

Expand

$$\frac{t^{7}}{s^{2}}$$

Solution Steps

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

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

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

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

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

$$s^{-4}t^{4}s^{2}t^{3}$$

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

$$s^{-2}t^{4}t^{3}$$

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

$$s^{-2}t^{7}$$