Solve (frac{(4x^{8}y^{4})^{4}*2x^{2}y^{6}}{x^8y^6*128x^9y})^2

$$( \frac { ( 4 x ^ { 8 } y ^ { 4 } ) ^ { 4 } \cdot 2 x ^ { 2 } y ^ { 6 } } { x ^ { 8 } y ^ { 6 } \cdot 128 x ^ { 9 } y } ) ^ { 2 }$$

Evaluate

$$16y^{30}x^{34}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$\left(\frac{\left(4x^{8}y^{4}\right)^{4}\times 2x^{2}y^{6}}{x^{17}y^{6}\times 128y}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\left(\frac{\left(4x^{8}y^{4}\right)^{4}\times 2x^{2}y^{6}}{x^{17}y^{7}\times 128}\right)^{2}$$

Cancel out 2x^{2}y^{6} in both numerator and denominator.

$$\left(\frac{\left(4y^{4}x^{8}\right)^{4}}{64yx^{15}}\right)^{2}$$

Expand \left(4y^{4}x^{8}\right)^{4}.

$$\left(\frac{4^{4}\left(y^{4}\right)^{4}\left(x^{8}\right)^{4}}{64yx^{15}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(\frac{4^{4}y^{16}\left(x^{8}\right)^{4}}{64yx^{15}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 4 to get 32.

$$\left(\frac{4^{4}y^{16}x^{32}}{64yx^{15}}\right)^{2}$$

Calculate 4 to the power of 4 and get 256.

$$\left(\frac{256y^{16}x^{32}}{64yx^{15}}\right)^{2}$$

Cancel out 64yx^{15} in both numerator and denominator.

$$\left(4y^{15}x^{17}\right)^{2}$$

Expand \left(4y^{15}x^{17}\right)^{2}.

$$4^{2}\left(y^{15}\right)^{2}\left(x^{17}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 2 to get 30.

$$4^{2}y^{30}\left(x^{17}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 17 and 2 to get 34.

$$4^{2}y^{30}x^{34}$$

Calculate 4 to the power of 2 and get 16.

$$16y^{30}x^{34}$$

Expand

$$16y^{30}x^{34}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$\left(\frac{\left(4x^{8}y^{4}\right)^{4}\times 2x^{2}y^{6}}{x^{17}y^{6}\times 128y}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\left(\frac{\left(4x^{8}y^{4}\right)^{4}\times 2x^{2}y^{6}}{x^{17}y^{7}\times 128}\right)^{2}$$

Cancel out 2x^{2}y^{6} in both numerator and denominator.

$$\left(\frac{\left(4y^{4}x^{8}\right)^{4}}{64yx^{15}}\right)^{2}$$

Expand \left(4y^{4}x^{8}\right)^{4}.

$$\left(\frac{4^{4}\left(y^{4}\right)^{4}\left(x^{8}\right)^{4}}{64yx^{15}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(\frac{4^{4}y^{16}\left(x^{8}\right)^{4}}{64yx^{15}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 4 to get 32.

$$\left(\frac{4^{4}y^{16}x^{32}}{64yx^{15}}\right)^{2}$$

Calculate 4 to the power of 4 and get 256.

$$\left(\frac{256y^{16}x^{32}}{64yx^{15}}\right)^{2}$$

Cancel out 64yx^{15} in both numerator and denominator.

$$\left(4y^{15}x^{17}\right)^{2}$$

Expand \left(4y^{15}x^{17}\right)^{2}.

$$4^{2}\left(y^{15}\right)^{2}\left(x^{17}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 2 to get 30.

$$4^{2}y^{30}\left(x^{17}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 17 and 2 to get 34.

$$4^{2}y^{30}x^{34}$$

Calculate 4 to the power of 2 and get 16.

$$16y^{30}x^{34}$$