Solve left(x^7*xright)^-5/{left(x^-3*y^4right)^3}

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

Evaluate

$$\frac{1}{y^{12}x^{31}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\left(x^{8}\right)^{-5}}{\left(x^{-3}y^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -5 to get -40.

$$\frac{x^{-40}}{\left(x^{-3}y^{4}\right)^{3}}$$

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

$$\frac{x^{-40}}{\left(x^{-3}\right)^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{x^{-40}}{x^{-9}\left(y^{4}\right)^{3}}$$

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

$$\frac{x^{-40}}{x^{-9}y^{12}}$$

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

$$\frac{1}{y^{12}x^{31}}$$

Expand

$$\frac{1}{y^{12}x^{31}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\left(x^{8}\right)^{-5}}{\left(x^{-3}y^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -5 to get -40.

$$\frac{x^{-40}}{\left(x^{-3}y^{4}\right)^{3}}$$

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

$$\frac{x^{-40}}{\left(x^{-3}\right)^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{x^{-40}}{x^{-9}\left(y^{4}\right)^{3}}$$

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

$$\frac{x^{-40}}{x^{-9}y^{12}}$$

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

$$\frac{1}{y^{12}x^{31}}$$