Solve B=frac{(frac{2^{-1}}{3})^{5}*(frac{2^{-1}}{3})^4}{((-2^-7/3)^2)^5}

$$B = \frac { ( \frac { 2 ^ { - 1 } } { 3 } ) ^ { 5 } \cdot ( \frac { 2 ^ { - 1 } } { 3 } ) ^ { 4 } } { ( ( - \frac { 2 ^ { - 7 } } { 3 } ) ^ { 2 } ) ^ { 5 } }$$

Solve for B

$$B=6917529027641081856$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$B=\frac{\left(\frac{2^{-1}}{3}\right)^{9}}{\left(\left(-\frac{2^{-7}}{3}\right)^{2}\right)^{5}}$$

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

$$B=\frac{\left(\frac{2^{-1}}{3}\right)^{9}}{\left(-\frac{2^{-7}}{3}\right)^{10}}$$

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

$$B=\frac{\left(\frac{\frac{1}{2}}{3}\right)^{9}}{\left(-\frac{2^{-7}}{3}\right)^{10}}$$

Express \frac{\frac{1}{2}}{3} as a single fraction.

$$B=\frac{\left(\frac{1}{2\times 3}\right)^{9}}{\left(-\frac{2^{-7}}{3}\right)^{10}}$$

Multiply 2 and 3 to get 6.

$$B=\frac{\left(\frac{1}{6}\right)^{9}}{\left(-\frac{2^{-7}}{3}\right)^{10}}$$

Calculate \frac{1}{6} to the power of 9 and get \frac{1}{10077696}.

$$B=\frac{\frac{1}{10077696}}{\left(-\frac{2^{-7}}{3}\right)^{10}}$$

Calculate 2 to the power of -7 and get \frac{1}{128}.

$$B=\frac{\frac{1}{10077696}}{\left(-\frac{\frac{1}{128}}{3}\right)^{10}}$$

Express \frac{\frac{1}{128}}{3} as a single fraction.

$$B=\frac{\frac{1}{10077696}}{\left(-\frac{1}{128\times 3}\right)^{10}}$$

Multiply 128 and 3 to get 384.

$$B=\frac{\frac{1}{10077696}}{\left(-\frac{1}{384}\right)^{10}}$$

Calculate -\frac{1}{384} to the power of 10 and get \frac{1}{69712754611742420055883776}.

$$B=\frac{\frac{1}{10077696}}{\frac{1}{69712754611742420055883776}}$$

Divide \frac{1}{10077696} by \frac{1}{69712754611742420055883776} by multiplying \frac{1}{10077696} by the reciprocal of \frac{1}{69712754611742420055883776}.

$$B=\frac{1}{10077696}\times 69712754611742420055883776$$

Multiply \frac{1}{10077696} and 69712754611742420055883776 to get 6917529027641081856.

$$B=6917529027641081856$$

Assign B

$$B≔6917529027641081856$$