Solve frac{(a^{5}b^{-3})^-5}{(6a^2b^-1)^-2}

$$\frac { ( a ^ { 5 } b ^ { - 3 } ) ^ { - 5 } } { ( 6 a ^ { 2 } b ^ { - 1 } ) ^ { - 2 } }$$

Evaluate

$$\frac{36b^{13}}{a^{21}}$$

Solution Steps

Expand \left(a^{5}b^{-3}\right)^{-5}.

$$\frac{\left(a^{5}\right)^{-5}\left(b^{-3}\right)^{-5}}{\left(6a^{2}b^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -5 to get -25.

$$\frac{a^{-25}\left(b^{-3}\right)^{-5}}{\left(6a^{2}b^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -5 to get 15.

$$\frac{a^{-25}b^{15}}{\left(6a^{2}b^{-1}\right)^{-2}}$$

Expand \left(6a^{2}b^{-1}\right)^{-2}.

$$\frac{a^{-25}b^{15}}{6^{-2}\left(a^{2}\right)^{-2}\left(b^{-1}\right)^{-2}}$$

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

$$\frac{a^{-25}b^{15}}{6^{-2}a^{-4}\left(b^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{a^{-25}b^{15}}{6^{-2}a^{-4}b^{2}}$$

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

$$\frac{a^{-25}b^{15}}{\frac{1}{36}a^{-4}b^{2}}$$

Cancel out b^{2} in both numerator and denominator.

$$\frac{a^{-25}b^{13}}{\frac{1}{36}a^{-4}}$$

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

$$\frac{b^{13}}{\frac{1}{36}a^{21}}$$

Expand

$$\frac{36b^{13}}{a^{21}}$$

Solution Steps

Expand \left(a^{5}b^{-3}\right)^{-5}.

$$\frac{\left(a^{5}\right)^{-5}\left(b^{-3}\right)^{-5}}{\left(6a^{2}b^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -5 to get -25.

$$\frac{a^{-25}\left(b^{-3}\right)^{-5}}{\left(6a^{2}b^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -5 to get 15.

$$\frac{a^{-25}b^{15}}{\left(6a^{2}b^{-1}\right)^{-2}}$$

Expand \left(6a^{2}b^{-1}\right)^{-2}.

$$\frac{a^{-25}b^{15}}{6^{-2}\left(a^{2}\right)^{-2}\left(b^{-1}\right)^{-2}}$$

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

$$\frac{a^{-25}b^{15}}{6^{-2}a^{-4}\left(b^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{a^{-25}b^{15}}{6^{-2}a^{-4}b^{2}}$$

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

$$\frac{a^{-25}b^{15}}{\frac{1}{36}a^{-4}b^{2}}$$

Cancel out b^{2} in both numerator and denominator.

$$\frac{a^{-25}b^{13}}{\frac{1}{36}a^{-4}}$$

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

$$\frac{b^{13}}{\frac{1}{36}a^{21}}$$