Solve (5a^4b^-3/4b^2)^-2

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

Evaluate

$$\frac{16b^{10}}{25a^{8}}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{5^{-2}a^{-8}}{\left(4b^{5}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}a^{-8}}{\left(4b^{5}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}a^{-8}}{4^{-2}\left(b^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{\frac{1}{25}a^{-8}}{4^{-2}b^{-10}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{25}a^{-8}}{\frac{1}{16}b^{-10}}$$

Expand

$$\frac{16b^{10}}{25a^{8}}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{5^{-2}a^{-8}}{\left(4b^{5}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}a^{-8}}{\left(4b^{5}\right)^{-2}}$$

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

$$\frac{\frac{1}{25}a^{-8}}{4^{-2}\left(b^{5}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{\frac{1}{25}a^{-8}}{4^{-2}b^{-10}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{25}a^{-8}}{\frac{1}{16}b^{-10}}$$