Solve (4y^6z^-5)^2

$$( 4 y ^ { 6 } z ^ { - 5 } ) ^ { 2 }$$

Evaluate

$$\frac{16y^{12}}{z^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4y^{6}z^{-5}\right)^{2}$$

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

$$4^{2}\left(y^{6}\right)^{2}\left(z^{-5}\right)^{2}$$

Raise 4 to the power 2.

$$16\left(y^{6}\right)^{2}\left(z^{-5}\right)^{2}$$

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

$$16y^{6\times 2}z^{-5\times 2}$$

Multiply 6 times 2.

$$16y^{12}z^{-5\times 2}$$

Multiply -5 times 2.

$$16y^{12}\times \frac{1}{z^{10}}$$

Expand

$$\frac{16y^{12}}{z^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4y^{6}z^{-5}\right)^{2}$$

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

$$4^{2}\left(y^{6}\right)^{2}\left(z^{-5}\right)^{2}$$

Raise 4 to the power 2.

$$16\left(y^{6}\right)^{2}\left(z^{-5}\right)^{2}$$

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

$$16y^{6\times 2}z^{-5\times 2}$$

Multiply 6 times 2.

$$16y^{12}z^{-5\times 2}$$

Multiply -5 times 2.

$$16y^{12}\times \frac{1}{z^{10}}$$