Solve (0.2x^4y^3)^2

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

Evaluate

$$\frac{y^{6}x^{8}}{25}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise 0.2 to the power 2.

$$0.04\left(x^{4}\right)^{2}\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$0.04x^{4\times 2}y^{3\times 2}$$

Multiply 4 times 2.

$$0.04x^{8}y^{3\times 2}$$

Multiply 3 times 2.

$$0.04x^{8}y^{6}$$

Expand

$$\frac{y^{6}x^{8}}{25}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise 0.2 to the power 2.

$$0.04\left(x^{4}\right)^{2}\left(y^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$0.04x^{4\times 2}y^{3\times 2}$$

Multiply 4 times 2.

$$0.04x^{8}y^{3\times 2}$$

Multiply 3 times 2.

$$0.04x^{8}y^{6}$$