Solve frac{(x^{7}x^{-4})^-5}{(x^-3xy^4)^3}

$$\frac { ( x ^ { 7 } x ^ { - 4 } ) ^ { - 5 } } { ( x ^ { - 3 } x y ^ { 4 } ) ^ { 3 } }$$

Evaluate

$$\frac{1}{x^{9}y^{12}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and -4 to get 3.

$$\frac{\left(x^{3}\right)^{-5}}{\left(x^{-3}xy^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -5 to get -15.

$$\frac{x^{-15}}{\left(x^{-3}xy^{4}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{x^{-15}}{\left(x^{-2}y^{4}\right)^{3}}$$

Expand \left(x^{-2}y^{4}\right)^{3}.

$$\frac{x^{-15}}{\left(x^{-2}\right)^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{x^{-15}}{x^{-6}\left(y^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{x^{-15}}{x^{-6}y^{12}}$$

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

$$\frac{1}{x^{9}y^{12}}$$

Expand

$$\frac{1}{x^{9}y^{12}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and -4 to get 3.

$$\frac{\left(x^{3}\right)^{-5}}{\left(x^{-3}xy^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -5 to get -15.

$$\frac{x^{-15}}{\left(x^{-3}xy^{4}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{x^{-15}}{\left(x^{-2}y^{4}\right)^{3}}$$

Expand \left(x^{-2}y^{4}\right)^{3}.

$$\frac{x^{-15}}{\left(x^{-2}\right)^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{x^{-15}}{x^{-6}\left(y^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{x^{-15}}{x^{-6}y^{12}}$$

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

$$\frac{1}{x^{9}y^{12}}$$