Solve (2ab^3/5x^4)^-2=

$$( \frac { 2 a b ^ { 3 } } { 5 x ^ { 4 } } ) ^ { - 2 } =$$

Evaluate

$$\frac{25x^{8}}{4a^{2}b^{6}}$$

Solution Steps

To raise \frac{2ab^{3}}{5x^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2ab^{3}\right)^{-2}}{\left(5x^{4}\right)^{-2}}$$

Expand \left(2ab^{3}\right)^{-2}.

$$\frac{2^{-2}a^{-2}\left(b^{3}\right)^{-2}}{\left(5x^{4}\right)^{-2}}$$

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

$$\frac{2^{-2}a^{-2}b^{-6}}{\left(5x^{4}\right)^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{\left(5x^{4}\right)^{-2}}$$

Expand \left(5x^{4}\right)^{-2}.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{5^{-2}\left(x^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{5^{-2}x^{-8}}$$

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

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{\frac{1}{25}x^{-8}}$$

Expand

$$\frac{25x^{8}}{4a^{2}b^{6}}$$

Solution Steps

To raise \frac{2ab^{3}}{5x^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2ab^{3}\right)^{-2}}{\left(5x^{4}\right)^{-2}}$$

Expand \left(2ab^{3}\right)^{-2}.

$$\frac{2^{-2}a^{-2}\left(b^{3}\right)^{-2}}{\left(5x^{4}\right)^{-2}}$$

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

$$\frac{2^{-2}a^{-2}b^{-6}}{\left(5x^{4}\right)^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{\left(5x^{4}\right)^{-2}}$$

Expand \left(5x^{4}\right)^{-2}.

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{5^{-2}\left(x^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{5^{-2}x^{-8}}$$

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

$$\frac{\frac{1}{4}a^{-2}b^{-6}}{\frac{1}{25}x^{-8}}$$