Solve (frac{24g^{-5}h^-2}{20g^9h^-10})^-2

$$( \frac { 24 g ^ { - 5 } h ^ { - 2 } } { 20 g ^ { 9 } h ^ { - 10 } } ) ^ { - 2 }$$

Evaluate

$$\frac{25g^{28}}{36h^{16}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\left(\frac{6g^{-5}h^{-2}}{5h^{-10}g^{9}}\right)^{-2}$$

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

$$\left(\frac{6g^{-5}h^{8}}{5g^{9}}\right)^{-2}$$

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

$$\left(\frac{6h^{8}}{5g^{14}}\right)^{-2}$$

To raise \frac{6h^{8}}{5g^{14}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6h^{8}\right)^{-2}}{\left(5g^{14}\right)^{-2}}$$

Expand \left(6h^{8}\right)^{-2}.

$$\frac{6^{-2}\left(h^{8}\right)^{-2}}{\left(5g^{14}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -2 to get -16.

$$\frac{6^{-2}h^{-16}}{\left(5g^{14}\right)^{-2}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{36}h^{-16}}{\left(5g^{14}\right)^{-2}}$$

Expand \left(5g^{14}\right)^{-2}.

$$\frac{\frac{1}{36}h^{-16}}{5^{-2}\left(g^{14}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 14 and -2 to get -28.

$$\frac{\frac{1}{36}h^{-16}}{5^{-2}g^{-28}}$$

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

$$\frac{\frac{1}{36}h^{-16}}{\frac{1}{25}g^{-28}}$$

Expand

$$\frac{25g^{28}}{36h^{16}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\left(\frac{6g^{-5}h^{-2}}{5h^{-10}g^{9}}\right)^{-2}$$

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

$$\left(\frac{6g^{-5}h^{8}}{5g^{9}}\right)^{-2}$$

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

$$\left(\frac{6h^{8}}{5g^{14}}\right)^{-2}$$

To raise \frac{6h^{8}}{5g^{14}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(6h^{8}\right)^{-2}}{\left(5g^{14}\right)^{-2}}$$

Expand \left(6h^{8}\right)^{-2}.

$$\frac{6^{-2}\left(h^{8}\right)^{-2}}{\left(5g^{14}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -2 to get -16.

$$\frac{6^{-2}h^{-16}}{\left(5g^{14}\right)^{-2}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{\frac{1}{36}h^{-16}}{\left(5g^{14}\right)^{-2}}$$

Expand \left(5g^{14}\right)^{-2}.

$$\frac{\frac{1}{36}h^{-16}}{5^{-2}\left(g^{14}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 14 and -2 to get -28.

$$\frac{\frac{1}{36}h^{-16}}{5^{-2}g^{-28}}$$

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

$$\frac{\frac{1}{36}h^{-16}}{\frac{1}{25}g^{-28}}$$