Solve (a^3)^2b:b/a^6=5

$$( a ^ { 3 } ) ^ { 2 } b : \frac { b } { a ^ { 6 } } = 5$$

Solve for b

$$b\neq 0$$

$$|a|=\sqrt[12]{5}$$

Steps for Solving Linear Equation

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

$$\frac{a^{6}b}{\frac{b}{a^{6}}}=5$$

Divide a^{6}b by \frac{b}{a^{6}} by multiplying a^{6}b by the reciprocal of \frac{b}{a^{6}}.

$$\frac{a^{6}ba^{6}}{b}=5$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{a^{12}b}{b}=5$$

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$a^{12}b=5b$$

Subtract 5b from both sides.

$$a^{12}b-5b=0$$

Combine all terms containing b.

$$\left(a^{12}-5\right)b=0$$

Divide 0 by a^{12}-5.

$$b=0$$

Variable b cannot be equal to 0.

$$b\in \emptyset$$

Solve for a

$$a=\sqrt[12]{5}$$

$$a=-\sqrt[12]{5}\text{, }b\neq 0$$