Solve frac{(5x^{2}y^-1)^-3}{(7x^-2y)^-2}

$$\frac { ( 5 x ^ { 2 } y ^ { - 1 } ) ^ { - 3 } } { ( 7 x ^ { - 2 } y ) ^ { - 2 } }$$

Evaluate

$$\frac{49y^{5}}{125x^{10}}$$

Solution Steps

Expand \left(5x^{2}y^{-1}\right)^{-3}.

$$\frac{5^{-3}\left(x^{2}\right)^{-3}\left(y^{-1}\right)^{-3}}{\left(7x^{-2}y\right)^{-2}}$$

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

$$\frac{5^{-3}x^{-6}\left(y^{-1}\right)^{-3}}{\left(7x^{-2}y\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{5^{-3}x^{-6}y^{3}}{\left(7x^{-2}y\right)^{-2}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}x^{-6}y^{3}}{\left(7x^{-2}y\right)^{-2}}$$

Expand \left(7x^{-2}y\right)^{-2}.

$$\frac{\frac{1}{125}x^{-6}y^{3}}{7^{-2}\left(x^{-2}\right)^{-2}y^{-2}}$$

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

$$\frac{\frac{1}{125}x^{-6}y^{3}}{7^{-2}x^{4}y^{-2}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{1}{125}x^{-6}y^{3}}{\frac{1}{49}x^{4}y^{-2}}$$

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

$$\frac{\frac{1}{125}x^{-6}y^{5}}{\frac{1}{49}x^{4}}$$

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

$$\frac{\frac{1}{125}y^{5}}{\frac{1}{49}x^{10}}$$

Expand

$$\frac{49y^{5}}{125x^{10}}$$

Solution Steps

Expand \left(5x^{2}y^{-1}\right)^{-3}.

$$\frac{5^{-3}\left(x^{2}\right)^{-3}\left(y^{-1}\right)^{-3}}{\left(7x^{-2}y\right)^{-2}}$$

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

$$\frac{5^{-3}x^{-6}\left(y^{-1}\right)^{-3}}{\left(7x^{-2}y\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{5^{-3}x^{-6}y^{3}}{\left(7x^{-2}y\right)^{-2}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}x^{-6}y^{3}}{\left(7x^{-2}y\right)^{-2}}$$

Expand \left(7x^{-2}y\right)^{-2}.

$$\frac{\frac{1}{125}x^{-6}y^{3}}{7^{-2}\left(x^{-2}\right)^{-2}y^{-2}}$$

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

$$\frac{\frac{1}{125}x^{-6}y^{3}}{7^{-2}x^{4}y^{-2}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{1}{125}x^{-6}y^{3}}{\frac{1}{49}x^{4}y^{-2}}$$

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

$$\frac{\frac{1}{125}x^{-6}y^{5}}{\frac{1}{49}x^{4}}$$

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

$$\frac{\frac{1}{125}y^{5}}{\frac{1}{49}x^{10}}$$