Solve frac{(-2a^{-4}b^{2})^{3}}{4ab^{10}}*frac{12^{-1}a^3b}{(3a^5b^0)^-2}

$$\frac { ( - 2 a ^ { - 4 } b ^ { 2 } ) ^ { 3 } } { 4 a b ^ { 10 } } \cdot \frac { 12 ^ { - 1 } a ^ { 3 } b } { ( 3 a ^ { 5 } b ^ { 0 } ) ^ { - 2 } }$$

Evaluate

$$-\frac{3}{2b^{3}}$$

Solution Steps

Expand \left(-2a^{-4}b^{2}\right)^{3}.

$$\frac{\left(-2\right)^{3}\left(a^{-4}\right)^{3}\left(b^{2}\right)^{3}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$\frac{\left(-2\right)^{3}a^{-12}\left(b^{2}\right)^{3}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

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

$$\frac{\left(-2\right)^{3}a^{-12}b^{6}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8a^{-12}b^{6}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Cancel out 4b^{6} in both numerator and denominator.

$$\frac{-2a^{-12}}{ab^{4}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

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

$$\frac{-2}{b^{4}a^{13}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Calculate 12 to the power of -1 and get \frac{1}{12}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Calculate b to the power of 0 and get 1.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\left(3a^{5}\times 1\right)^{-2}}$$

Multiply 3 and 1 to get 3.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\left(3a^{5}\right)^{-2}}$$

Expand \left(3a^{5}\right)^{-2}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{3^{-2}\left(a^{5}\right)^{-2}}$$

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

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{3^{-2}a^{-10}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\frac{1}{9}a^{-10}}$$

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

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}ba^{13}}{\frac{1}{9}}$$

Divide \frac{1}{12}ba^{13} by \frac{1}{9} by multiplying \frac{1}{12}ba^{13} by the reciprocal of \frac{1}{9}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{1}{12}ba^{13}\times 9$$

Multiply \frac{1}{12} and 9 to get \frac{3}{4}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{3}{4}ba^{13}$$

Multiply \frac{-2}{b^{4}a^{13}} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 3}{b^{4}a^{13}\times 4}ba^{13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3}{2b^{4}a^{13}}ba^{13}$$

Express \frac{-3}{2b^{4}a^{13}}b as a single fraction.

$$\frac{-3b}{2b^{4}a^{13}}a^{13}$$

Cancel out b in both numerator and denominator.

$$\frac{-3}{2b^{3}a^{13}}a^{13}$$

Express \frac{-3}{2b^{3}a^{13}}a^{13} as a single fraction.

$$\frac{-3a^{13}}{2b^{3}a^{13}}$$

Cancel out a^{13} in both numerator and denominator.

$$\frac{-3}{2b^{3}}$$

Expand

$$-\frac{3}{2b^{3}}$$

Solution Steps

Expand \left(-2a^{-4}b^{2}\right)^{3}.

$$\frac{\left(-2\right)^{3}\left(a^{-4}\right)^{3}\left(b^{2}\right)^{3}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$\frac{\left(-2\right)^{3}a^{-12}\left(b^{2}\right)^{3}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

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

$$\frac{\left(-2\right)^{3}a^{-12}b^{6}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8a^{-12}b^{6}}{4ab^{10}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Cancel out 4b^{6} in both numerator and denominator.

$$\frac{-2a^{-12}}{ab^{4}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

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

$$\frac{-2}{b^{4}a^{13}}\times \frac{12^{-1}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Calculate 12 to the power of -1 and get \frac{1}{12}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\left(3a^{5}b^{0}\right)^{-2}}$$

Calculate b to the power of 0 and get 1.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\left(3a^{5}\times 1\right)^{-2}}$$

Multiply 3 and 1 to get 3.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\left(3a^{5}\right)^{-2}}$$

Expand \left(3a^{5}\right)^{-2}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{3^{-2}\left(a^{5}\right)^{-2}}$$

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

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{3^{-2}a^{-10}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}a^{3}b}{\frac{1}{9}a^{-10}}$$

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

$$\frac{-2}{b^{4}a^{13}}\times \frac{\frac{1}{12}ba^{13}}{\frac{1}{9}}$$

Divide \frac{1}{12}ba^{13} by \frac{1}{9} by multiplying \frac{1}{12}ba^{13} by the reciprocal of \frac{1}{9}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{1}{12}ba^{13}\times 9$$

Multiply \frac{1}{12} and 9 to get \frac{3}{4}.

$$\frac{-2}{b^{4}a^{13}}\times \frac{3}{4}ba^{13}$$

Multiply \frac{-2}{b^{4}a^{13}} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 3}{b^{4}a^{13}\times 4}ba^{13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3}{2b^{4}a^{13}}ba^{13}$$

Express \frac{-3}{2b^{4}a^{13}}b as a single fraction.

$$\frac{-3b}{2b^{4}a^{13}}a^{13}$$

Cancel out b in both numerator and denominator.

$$\frac{-3}{2b^{3}a^{13}}a^{13}$$

Express \frac{-3}{2b^{3}a^{13}}a^{13} as a single fraction.

$$\frac{-3a^{13}}{2b^{3}a^{13}}$$

Cancel out a^{13} in both numerator and denominator.

$$\frac{-3}{2b^{3}}$$