Solve 5(g^{4}h^3)^-2div2g^-4h^-6

$$5 ( g ^ { 4 } h ^ { 3 } ) ^ { - 2 } \div 2 g ^ { - 4 } h ^ { - 6 }$$

Evaluate

$$\frac{5}{2\left(gh\right)^{12}}$$

Solution Steps

Expand \left(g^{4}h^{3}\right)^{-2}.

$$\frac{5\left(g^{4}\right)^{-2}\left(h^{3}\right)^{-2}}{2}g^{-4}h^{-6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{5g^{-8}\left(h^{3}\right)^{-2}}{2}g^{-4}h^{-6}$$

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

$$\frac{5g^{-8}h^{-6}}{2}g^{-4}h^{-6}$$

Express \frac{5g^{-8}h^{-6}}{2}g^{-4} as a single fraction.

$$\frac{5g^{-8}h^{-6}g^{-4}}{2}h^{-6}$$

Express \frac{5g^{-8}h^{-6}g^{-4}}{2}h^{-6} as a single fraction.

$$\frac{5g^{-8}h^{-6}g^{-4}h^{-6}}{2}$$

To multiply powers of the same base, add their exponents. Add -8 and -4 to get -12.

$$\frac{5g^{-12}h^{-6}h^{-6}}{2}$$

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$\frac{5g^{-12}h^{-12}}{2}$$

Expand

$$\frac{5}{2\left(gh\right)^{12}}$$

Solution Steps

Expand \left(g^{4}h^{3}\right)^{-2}.

$$\frac{5\left(g^{4}\right)^{-2}\left(h^{3}\right)^{-2}}{2}g^{-4}h^{-6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{5g^{-8}\left(h^{3}\right)^{-2}}{2}g^{-4}h^{-6}$$

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

$$\frac{5g^{-8}h^{-6}}{2}g^{-4}h^{-6}$$

Express \frac{5g^{-8}h^{-6}}{2}g^{-4} as a single fraction.

$$\frac{5g^{-8}h^{-6}g^{-4}}{2}h^{-6}$$

Express \frac{5g^{-8}h^{-6}g^{-4}}{2}h^{-6} as a single fraction.

$$\frac{5g^{-8}h^{-6}g^{-4}h^{-6}}{2}$$

To multiply powers of the same base, add their exponents. Add -8 and -4 to get -12.

$$\frac{5g^{-12}h^{-6}h^{-6}}{2}$$

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$\frac{5g^{-12}h^{-12}}{2}$$