Solve (frac{a^{-6}b^-5}{4a^-8b^-3})^-2

$$( \frac { a ^ { - 6 } b ^ { - 5 } } { 4 a ^ { - 8 } b ^ { - 3 } } ) ^ { - 2 }$$

Evaluate

$$16\times \left(\frac{b}{a}\right)^{4}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{a^{-4}}{4^{-2}b^{-4}}$$

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

$$\frac{a^{-4}}{\frac{1}{16}b^{-4}}$$

Expand

$$16\times \left(\frac{b}{a}\right)^{4}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{a^{-4}}{4^{-2}b^{-4}}$$

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

$$\frac{a^{-4}}{\frac{1}{16}b^{-4}}$$