Solve (frac{u^{5}v^9}{2}*8v^4u^9)^3

$$( \frac { u ^ { 5 } v ^ { 9 } } { 2 } \times 8 v ^ { 4 } u ^ { 9 } ) ^ { 3 }$$

Evaluate

$$64v^{39}u^{42}$$

Solution Steps

Cancel out 2, the greatest common factor in 8 and 2.

$$\left(4u^{5}v^{9}v^{4}u^{9}\right)^{3}$$

Expand \left(4u^{5}v^{9}v^{4}u^{9}\right)^{3}.

$$4^{3}\left(u^{5}\right)^{3}\left(v^{9}\right)^{3}\left(v^{4}\right)^{3}\left(u^{9}\right)^{3}$$

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

$$4^{3}u^{15}\left(v^{9}\right)^{3}\left(v^{4}\right)^{3}\left(u^{9}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$4^{3}u^{15}v^{27}\left(v^{4}\right)^{3}\left(u^{9}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$4^{3}u^{15}v^{27}v^{12}\left(u^{9}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$4^{3}u^{15}v^{27}v^{12}u^{27}$$

To multiply powers of the same base, add their exponents. Add 15 and 27 to get 42.

$$4^{3}u^{42}v^{27}v^{12}$$

To multiply powers of the same base, add their exponents. Add 27 and 12 to get 39.

$$4^{3}u^{42}v^{39}$$

Calculate 4 to the power of 3 and get 64.

$$64u^{42}v^{39}$$

Expand

$$64v^{39}u^{42}$$

Solution Steps

Cancel out 2, the greatest common factor in 8 and 2.

$$\left(4u^{5}v^{9}v^{4}u^{9}\right)^{3}$$

Expand \left(4u^{5}v^{9}v^{4}u^{9}\right)^{3}.

$$4^{3}\left(u^{5}\right)^{3}\left(v^{9}\right)^{3}\left(v^{4}\right)^{3}\left(u^{9}\right)^{3}$$

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

$$4^{3}u^{15}\left(v^{9}\right)^{3}\left(v^{4}\right)^{3}\left(u^{9}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$4^{3}u^{15}v^{27}\left(v^{4}\right)^{3}\left(u^{9}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$4^{3}u^{15}v^{27}v^{12}\left(u^{9}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$4^{3}u^{15}v^{27}v^{12}u^{27}$$

To multiply powers of the same base, add their exponents. Add 15 and 27 to get 42.

$$4^{3}u^{42}v^{27}v^{12}$$

To multiply powers of the same base, add their exponents. Add 27 and 12 to get 39.

$$4^{3}u^{42}v^{39}$$

Calculate 4 to the power of 3 and get 64.

$$64u^{42}v^{39}$$