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

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

Evaluate

$$\frac{25y^{9}}{x^{5}}$$

Solution Steps

Expand \left(5x^{2}y^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$5^{2}x^{4}y^{6}\left(x^{-3}y\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{4}y^{6}\left(x^{-3}y\right)^{3}$$

Expand \left(x^{-3}y\right)^{3}.

$$25x^{4}y^{6}\left(x^{-3}\right)^{3}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$25x^{4}y^{6}x^{-9}y^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and -9 to get -5.

$$25x^{-5}y^{6}y^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$25x^{-5}y^{9}$$

Expand

$$\frac{25y^{9}}{x^{5}}$$

Solution Steps

Expand \left(5x^{2}y^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$5^{2}x^{4}y^{6}\left(x^{-3}y\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{4}y^{6}\left(x^{-3}y\right)^{3}$$

Expand \left(x^{-3}y\right)^{3}.

$$25x^{4}y^{6}\left(x^{-3}\right)^{3}y^{3}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$25x^{4}y^{6}x^{-9}y^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and -9 to get -5.

$$25x^{-5}y^{6}y^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$25x^{-5}y^{9}$$