Solve (frac{a^{5}}{b^-16})(b^4/a^-3)^-2

$$( \frac { a ^ { 5 } } { b ^ { - 16 } } ) ( \frac { b ^ { 4 } } { a ^ { - 3 } } ) ^ { - 2 }$$

Evaluate

$$\frac{b^{8}}{a}$$

Solution Steps

To raise \frac{b^{4}}{a^{-3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{5}}{b^{-16}}\times \frac{\left(b^{4}\right)^{-2}}{\left(a^{-3}\right)^{-2}}$$

Multiply \frac{a^{5}}{b^{-16}} times \frac{\left(b^{4}\right)^{-2}}{\left(a^{-3}\right)^{-2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{5}\left(b^{4}\right)^{-2}}{b^{-16}\left(a^{-3}\right)^{-2}}$$

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

$$\frac{a^{5}b^{-8}}{b^{-16}\left(a^{-3}\right)^{-2}}$$

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

$$\frac{a^{5}b^{-8}}{b^{-16}a^{6}}$$

Cancel out a^{5} in both numerator and denominator.

$$\frac{b^{-8}}{b^{-16}a}$$

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

$$\frac{b^{8}}{a}$$

Expand

$$\frac{b^{8}}{a}$$

Solution Steps

To raise \frac{b^{4}}{a^{-3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{a^{5}}{b^{-16}}\times \frac{\left(b^{4}\right)^{-2}}{\left(a^{-3}\right)^{-2}}$$

Multiply \frac{a^{5}}{b^{-16}} times \frac{\left(b^{4}\right)^{-2}}{\left(a^{-3}\right)^{-2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{5}\left(b^{4}\right)^{-2}}{b^{-16}\left(a^{-3}\right)^{-2}}$$

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

$$\frac{a^{5}b^{-8}}{b^{-16}\left(a^{-3}\right)^{-2}}$$

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

$$\frac{a^{5}b^{-8}}{b^{-16}a^{6}}$$

Cancel out a^{5} in both numerator and denominator.

$$\frac{b^{-8}}{b^{-16}a}$$

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

$$\frac{b^{8}}{a}$$