Solve (-4y^-3z^2)^2

$$( - 4 y ^ { - 3 } z ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{16z^{4}}{y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-4y^{-3}z^{2}\right)^{2}$$

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

$$\left(-4\right)^{2}\left(y^{-3}\right)^{2}\left(z^{2}\right)^{2}$$

Raise -4 to the power 2.

$$16\left(y^{-3}\right)^{2}\left(z^{2}\right)^{2}$$

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

$$16y^{-3\times 2}z^{2\times 2}$$

Multiply -3 times 2.

$$16\times \frac{1}{y^{6}}z^{2\times 2}$$

Multiply 2 times 2.

$$16\times \frac{1}{y^{6}}z^{4}$$

Expand

$$\frac{16z^{4}}{y^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-4y^{-3}z^{2}\right)^{2}$$

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

$$\left(-4\right)^{2}\left(y^{-3}\right)^{2}\left(z^{2}\right)^{2}$$

Raise -4 to the power 2.

$$16\left(y^{-3}\right)^{2}\left(z^{2}\right)^{2}$$

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

$$16y^{-3\times 2}z^{2\times 2}$$

Multiply -3 times 2.

$$16\times \frac{1}{y^{6}}z^{2\times 2}$$

Multiply 2 times 2.

$$16\times \frac{1}{y^{6}}z^{4}$$