Solve (frac{x^{2}y^{5}a^{10}}{x^{-4}ya^{5}})^{5}*(x^-2y^3a/a^-2)^-3

$$( \frac { x ^ { 2 } y ^ { 5 } a ^ { 10 } } { x ^ { - 4 } y a ^ { 5 } } ) ^ { 5 } \cdot ( \frac { x ^ { - 2 } y ^ { 3 } a } { a ^ { - 2 } } ) ^ { - 3 }$$

Evaluate

$$y^{11}a^{16}x^{36}$$

Solution Steps

Cancel out ya^{5} in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Expand \left(y^{4}a^{5}x^{6}\right)^{5}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$y^{20}\left(a^{5}\right)^{5}\left(x^{6}\right)^{5}\times \left(\frac{x^{-2}y^{3}a}{a^{-2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$y^{20}a^{25}\left(x^{6}\right)^{5}\times \left(\frac{x^{-2}y^{3}a}{a^{-2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$y^{20}a^{25}x^{30}\times \left(\frac{x^{-2}y^{3}a}{a^{-2}}\right)^{-3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$y^{20}a^{25}x^{30}\left(x^{-2}a^{3}y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}\left(x^{-2}\right)^{-3}\left(a^{3}\right)^{-3}\left(y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}x^{6}\left(a^{3}\right)^{-3}\left(y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}x^{6}a^{-9}\left(y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}x^{6}a^{-9}y^{-9}$$

To multiply powers of the same base, add their exponents. Add 30 and 6 to get 36.

$$y^{20}a^{25}x^{36}a^{-9}y^{-9}$$

To multiply powers of the same base, add their exponents. Add 25 and -9 to get 16.

$$y^{20}a^{16}x^{36}y^{-9}$$

To multiply powers of the same base, add their exponents. Add 20 and -9 to get 11.

$$y^{11}a^{16}x^{36}$$

Expand

$$y^{11}a^{16}x^{36}$$

Solution Steps

Cancel out ya^{5} in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Expand \left(y^{4}a^{5}x^{6}\right)^{5}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$y^{20}\left(a^{5}\right)^{5}\left(x^{6}\right)^{5}\times \left(\frac{x^{-2}y^{3}a}{a^{-2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$y^{20}a^{25}\left(x^{6}\right)^{5}\times \left(\frac{x^{-2}y^{3}a}{a^{-2}}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$y^{20}a^{25}x^{30}\times \left(\frac{x^{-2}y^{3}a}{a^{-2}}\right)^{-3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$y^{20}a^{25}x^{30}\left(x^{-2}a^{3}y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}\left(x^{-2}\right)^{-3}\left(a^{3}\right)^{-3}\left(y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}x^{6}\left(a^{3}\right)^{-3}\left(y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}x^{6}a^{-9}\left(y^{3}\right)^{-3}$$

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

$$y^{20}a^{25}x^{30}x^{6}a^{-9}y^{-9}$$

To multiply powers of the same base, add their exponents. Add 30 and 6 to get 36.

$$y^{20}a^{25}x^{36}a^{-9}y^{-9}$$

To multiply powers of the same base, add their exponents. Add 25 and -9 to get 16.

$$y^{20}a^{16}x^{36}y^{-9}$$

To multiply powers of the same base, add their exponents. Add 20 and -9 to get 11.

$$y^{11}a^{16}x^{36}$$