Solve (u^{2}v^-7)^4(u^5)^3=

$$( u ^ { 2 } v ^ { - 7 } ) ^ { 4 } ( u ^ { 5 } ) ^ { 3 } =$$

Evaluate

$$\frac{u^{23}}{v^{28}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\left(u^{2}v^{-7}\right)^{4}u^{15}$$

Expand \left(u^{2}v^{-7}\right)^{4}.

$$\left(u^{2}\right)^{4}\left(v^{-7}\right)^{4}u^{15}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$u^{8}\left(v^{-7}\right)^{4}u^{15}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 4 to get -28.

$$u^{8}v^{-28}u^{15}$$

To multiply powers of the same base, add their exponents. Add 8 and 15 to get 23.

$$u^{23}v^{-28}$$

Expand

$$\frac{u^{23}}{v^{28}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\left(u^{2}v^{-7}\right)^{4}u^{15}$$

Expand \left(u^{2}v^{-7}\right)^{4}.

$$\left(u^{2}\right)^{4}\left(v^{-7}\right)^{4}u^{15}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$u^{8}\left(v^{-7}\right)^{4}u^{15}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 4 to get -28.

$$u^{8}v^{-28}u^{15}$$

To multiply powers of the same base, add their exponents. Add 8 and 15 to get 23.

$$u^{23}v^{-28}$$