Solve (2)(0.3x^{3}y^{4})^2*(0.2x^4y^3)^2

$$( 2 ) ( 0.3 x ^ { 3 } y ^ { 4 } ) ^ { 2 } \cdot ( 0.2 x ^ { 4 } y ^ { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{9\left(xy\right)^{14}}{1250}$$

Solution Steps

Expand \left(0.3x^{3}y^{4}\right)^{2}.

$$2\times 0.3^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}\times \left(0.2x^{4}y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$2\times 0.3^{2}x^{6}\left(y^{4}\right)^{2}\times \left(0.2x^{4}y^{3}\right)^{2}$$

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

$$2\times 0.3^{2}x^{6}y^{8}\times \left(0.2x^{4}y^{3}\right)^{2}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$2\times 0.09x^{6}y^{8}\times \left(0.2x^{4}y^{3}\right)^{2}$$

Multiply 2 and 0.09 to get 0.18.

$$0.18x^{6}y^{8}\times \left(0.2x^{4}y^{3}\right)^{2}$$

Expand \left(0.2x^{4}y^{3}\right)^{2}.

$$0.18x^{6}y^{8}\times 0.2^{2}\left(x^{4}\right)^{2}\left(y^{3}\right)^{2}$$

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

$$0.18x^{6}y^{8}\times 0.2^{2}x^{8}\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$0.18x^{6}y^{8}\times 0.2^{2}x^{8}y^{6}$$

Calculate 0.2 to the power of 2 and get 0.04.

$$0.18x^{6}y^{8}\times 0.04x^{8}y^{6}$$

Multiply 0.18 and 0.04 to get 0.0072.

$$0.0072x^{6}y^{8}x^{8}y^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$0.0072x^{14}y^{8}y^{6}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$0.0072x^{14}y^{14}$$

Expand

$$\frac{9\left(xy\right)^{14}}{1250}$$

Solution Steps

Expand \left(0.3x^{3}y^{4}\right)^{2}.

$$2\times 0.3^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}\times \left(0.2x^{4}y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$2\times 0.3^{2}x^{6}\left(y^{4}\right)^{2}\times \left(0.2x^{4}y^{3}\right)^{2}$$

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

$$2\times 0.3^{2}x^{6}y^{8}\times \left(0.2x^{4}y^{3}\right)^{2}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$2\times 0.09x^{6}y^{8}\times \left(0.2x^{4}y^{3}\right)^{2}$$

Multiply 2 and 0.09 to get 0.18.

$$0.18x^{6}y^{8}\times \left(0.2x^{4}y^{3}\right)^{2}$$

Expand \left(0.2x^{4}y^{3}\right)^{2}.

$$0.18x^{6}y^{8}\times 0.2^{2}\left(x^{4}\right)^{2}\left(y^{3}\right)^{2}$$

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

$$0.18x^{6}y^{8}\times 0.2^{2}x^{8}\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$0.18x^{6}y^{8}\times 0.2^{2}x^{8}y^{6}$$

Calculate 0.2 to the power of 2 and get 0.04.

$$0.18x^{6}y^{8}\times 0.04x^{8}y^{6}$$

Multiply 0.18 and 0.04 to get 0.0072.

$$0.0072x^{6}y^{8}x^{8}y^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$0.0072x^{14}y^{8}y^{6}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$0.0072x^{14}y^{14}$$