Solve 7t^{11}u^3(-4t^-9)^2u^-5

$$7 t ^ { 11 } u ^ { 3 } ( - 4 t ^ { - 9 } ) ^ { 2 } u ^ { - 5 }$$

Evaluate

$$\frac{112}{u^{2}t^{7}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

$$7t^{11}u^{-2}\left(-4t^{-9}\right)^{2}$$

Expand \left(-4t^{-9}\right)^{2}.

$$7t^{11}u^{-2}\left(-4\right)^{2}\left(t^{-9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -9 and 2 to get -18.

$$7t^{11}u^{-2}\left(-4\right)^{2}t^{-18}$$

Calculate -4 to the power of 2 and get 16.

$$7t^{11}u^{-2}\times 16t^{-18}$$

Multiply 7 and 16 to get 112.

$$112t^{11}u^{-2}t^{-18}$$

To multiply powers of the same base, add their exponents. Add 11 and -18 to get -7.

$$112t^{-7}u^{-2}$$

Expand

$$\frac{112}{u^{2}t^{7}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

$$7t^{11}u^{-2}\left(-4t^{-9}\right)^{2}$$

Expand \left(-4t^{-9}\right)^{2}.

$$7t^{11}u^{-2}\left(-4\right)^{2}\left(t^{-9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -9 and 2 to get -18.

$$7t^{11}u^{-2}\left(-4\right)^{2}t^{-18}$$

Calculate -4 to the power of 2 and get 16.

$$7t^{11}u^{-2}\times 16t^{-18}$$

Multiply 7 and 16 to get 112.

$$112t^{11}u^{-2}t^{-18}$$

To multiply powers of the same base, add their exponents. Add 11 and -18 to get -7.

$$112t^{-7}u^{-2}$$