Solve (5)(frac{2x^{6}y^{5}*2x^{3}y^5}{2x^4y^4})^6

$$( 5 ) ( \frac { 2 x ^ { 6 } y ^ { 5 } \cdot 2 x ^ { 3 } y ^ { 5 } } { 2 x ^ { 4 } y ^ { 4 } } ) ^ { 6 }$$

Evaluate

$$320x^{30}y^{36}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$5\times \left(\frac{2x^{9}y^{5}\times 2y^{5}}{2x^{4}y^{4}}\right)^{6}$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$5\times \left(\frac{2x^{9}y^{10}\times 2}{2x^{4}y^{4}}\right)^{6}$$

Cancel out 2x^{4}y^{4} in both numerator and denominator.

$$5\times \left(2x^{5}y^{6}\right)^{6}$$

Expand \left(2x^{5}y^{6}\right)^{6}.

$$5\times 2^{6}\left(x^{5}\right)^{6}\left(y^{6}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 6 to get 30.

$$5\times 2^{6}x^{30}\left(y^{6}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 6 to get 36.

$$5\times 2^{6}x^{30}y^{36}$$

Calculate 2 to the power of 6 and get 64.

$$5\times 64x^{30}y^{36}$$

Multiply 5 and 64 to get 320.

$$320x^{30}y^{36}$$

Expand

$$320x^{30}y^{36}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$5\times \left(\frac{2x^{9}y^{5}\times 2y^{5}}{2x^{4}y^{4}}\right)^{6}$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$5\times \left(\frac{2x^{9}y^{10}\times 2}{2x^{4}y^{4}}\right)^{6}$$

Cancel out 2x^{4}y^{4} in both numerator and denominator.

$$5\times \left(2x^{5}y^{6}\right)^{6}$$

Expand \left(2x^{5}y^{6}\right)^{6}.

$$5\times 2^{6}\left(x^{5}\right)^{6}\left(y^{6}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 6 to get 30.

$$5\times 2^{6}x^{30}\left(y^{6}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 6 to get 36.

$$5\times 2^{6}x^{30}y^{36}$$

Calculate 2 to the power of 6 and get 64.

$$5\times 64x^{30}y^{36}$$

Multiply 5 and 64 to get 320.

$$320x^{30}y^{36}$$