Solve (5a^4y^-3)^-2

$$( 5 a ^ { 4 } y ^ { - 3 } ) ^ { - 2 }$$

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5a^{4}y^{-3}\right)^{-2}$$

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

$$5^{-2}\left(a^{4}\right)^{-2}\left(y^{-3}\right)^{-2}$$

Raise 5 to the power -2.

$$\frac{1}{25}\left(a^{4}\right)^{-2}\left(y^{-3}\right)^{-2}$$

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

$$\frac{1}{25}a^{4\left(-2\right)}y^{-3\left(-2\right)}$$

Multiply 4 times -2.

$$\frac{1}{25}\times \frac{1}{a^{8}}y^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{25}\times \frac{1}{a^{8}}y^{6}$$

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5a^{4}y^{-3}\right)^{-2}$$

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

$$5^{-2}\left(a^{4}\right)^{-2}\left(y^{-3}\right)^{-2}$$

Raise 5 to the power -2.

$$\frac{1}{25}\left(a^{4}\right)^{-2}\left(y^{-3}\right)^{-2}$$

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

$$\frac{1}{25}a^{4\left(-2\right)}y^{-3\left(-2\right)}$$

Multiply 4 times -2.

$$\frac{1}{25}\times \frac{1}{a^{8}}y^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{25}\times \frac{1}{a^{8}}y^{6}$$