Solve (3x^5y^-3)^2

$$( 3 x ^ { 5 } y ^ { - 3 } ) ^ { 2 }$$

Evaluate

$$\frac{9x^{10}}{y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{5}y^{-3}\right)^{2}$$

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

$$3^{2}\left(x^{5}\right)^{2}\left(y^{-3}\right)^{2}$$

Raise 3 to the power 2.

$$9\left(x^{5}\right)^{2}\left(y^{-3}\right)^{2}$$

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

$$9x^{5\times 2}y^{-3\times 2}$$

Multiply 5 times 2.

$$9x^{10}y^{-3\times 2}$$

Multiply -3 times 2.

$$9x^{10}\times \frac{1}{y^{6}}$$

Expand

$$\frac{9x^{10}}{y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3x^{5}y^{-3}\right)^{2}$$

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

$$3^{2}\left(x^{5}\right)^{2}\left(y^{-3}\right)^{2}$$

Raise 3 to the power 2.

$$9\left(x^{5}\right)^{2}\left(y^{-3}\right)^{2}$$

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

$$9x^{5\times 2}y^{-3\times 2}$$

Multiply 5 times 2.

$$9x^{10}y^{-3\times 2}$$

Multiply -3 times 2.

$$9x^{10}\times \frac{1}{y^{6}}$$