Solve (32x^5y^-10)^4

$$( 32 x ^ { 5 } y ^ { - 10 } ) ^ { 4 }$$

Evaluate

$$\frac{1048576x^{20}}{y^{40}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(32x^{5}y^{-10}\right)^{4}$$

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

$$32^{4}\left(x^{5}\right)^{4}\left(y^{-10}\right)^{4}$$

Raise 32 to the power 4.

$$1048576\left(x^{5}\right)^{4}\left(y^{-10}\right)^{4}$$

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

$$1048576x^{5\times 4}y^{-10\times 4}$$

Multiply 5 times 4.

$$1048576x^{20}y^{-10\times 4}$$

Multiply -10 times 4.

$$1048576x^{20}\times \frac{1}{y^{40}}$$

Expand

$$\frac{1048576x^{20}}{y^{40}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(32x^{5}y^{-10}\right)^{4}$$

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

$$32^{4}\left(x^{5}\right)^{4}\left(y^{-10}\right)^{4}$$

Raise 32 to the power 4.

$$1048576\left(x^{5}\right)^{4}\left(y^{-10}\right)^{4}$$

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

$$1048576x^{5\times 4}y^{-10\times 4}$$

Multiply 5 times 4.

$$1048576x^{20}y^{-10\times 4}$$

Multiply -10 times 4.

$$1048576x^{20}\times \frac{1}{y^{40}}$$