Solve frac{(5x^{3}y^-2)^-2}{25x^3y^4}

$$\frac { ( 5 x ^ { 3 } y ^ { - 2 } ) ^ { - 2 } } { 25 x ^ { 3 } y ^ { 4 } }$$

Evaluate

$$\frac{1}{625x^{9}}$$

Solution Steps

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

$$\frac{5^{-2}\left(x^{3}\right)^{-2}\left(y^{-2}\right)^{-2}}{25x^{3}y^{4}}$$

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

$$\frac{5^{-2}x^{-6}\left(y^{-2}\right)^{-2}}{25x^{3}y^{4}}$$

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

$$\frac{5^{-2}x^{-6}y^{4}}{25x^{3}y^{4}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{-6}y^{4}}{25x^{3}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{\frac{1}{25}x^{-6}}{25x^{3}}$$

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

$$\frac{\frac{1}{25}}{25x^{9}}$$

Express \frac{\frac{1}{25}}{25x^{9}} as a single fraction.

$$\frac{1}{25\times 25x^{9}}$$

Multiply 25 and 25 to get 625.

$$\frac{1}{625x^{9}}$$

Expand

$$\frac{1}{625x^{9}}$$

Solution Steps

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

$$\frac{5^{-2}\left(x^{3}\right)^{-2}\left(y^{-2}\right)^{-2}}{25x^{3}y^{4}}$$

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

$$\frac{5^{-2}x^{-6}\left(y^{-2}\right)^{-2}}{25x^{3}y^{4}}$$

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

$$\frac{5^{-2}x^{-6}y^{4}}{25x^{3}y^{4}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{\frac{1}{25}x^{-6}y^{4}}{25x^{3}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{\frac{1}{25}x^{-6}}{25x^{3}}$$

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

$$\frac{\frac{1}{25}}{25x^{9}}$$

Express \frac{\frac{1}{25}}{25x^{9}} as a single fraction.

$$\frac{1}{25\times 25x^{9}}$$

Multiply 25 and 25 to get 625.

$$\frac{1}{625x^{9}}$$