Solve B=(frac{8*x^{8}}{3^{3}})^2:(3^2/2*x^5)^-3

$$B = ( \frac { 8 \cdot x ^ { 8 } } { 3 ^ { 3 } } ) ^ { 2 } : ( \frac { 3 ^ { 2 } } { 2 \cdot x ^ { 5 } } ) ^ { - 3 }$$

Solve for B

$$B=8x$$

$$x\neq 0$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$B=\frac{\left(\frac{8x^{8}}{27}\right)^{2}}{\left(\frac{3^{2}}{2x^{5}}\right)^{-3}}$$

To raise \frac{8x^{8}}{27} to a power, raise both numerator and denominator to the power and then divide.

$$B=\frac{\frac{\left(8x^{8}\right)^{2}}{27^{2}}}{\left(\frac{3^{2}}{2x^{5}}\right)^{-3}}$$

Calculate 3 to the power of 2 and get 9.

$$B=\frac{\frac{\left(8x^{8}\right)^{2}}{27^{2}}}{\left(\frac{9}{2x^{5}}\right)^{-3}}$$

To raise \frac{9}{2x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$B=\frac{\frac{\left(8x^{8}\right)^{2}}{27^{2}}}{\frac{9^{-3}}{\left(2x^{5}\right)^{-3}}}$$

Divide \frac{\left(8x^{8}\right)^{2}}{27^{2}} by \frac{9^{-3}}{\left(2x^{5}\right)^{-3}} by multiplying \frac{\left(8x^{8}\right)^{2}}{27^{2}} by the reciprocal of \frac{9^{-3}}{\left(2x^{5}\right)^{-3}}.

$$B=\frac{\left(8x^{8}\right)^{2}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

Expand \left(8x^{8}\right)^{2}.

$$B=\frac{8^{2}\left(x^{8}\right)^{2}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$B=\frac{8^{2}x^{16}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

Calculate 8 to the power of 2 and get 64.

$$B=\frac{64x^{16}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

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

$$B=\frac{64x^{16}\times 2^{-3}\left(x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

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

$$B=\frac{64x^{16}\times 2^{-3}x^{-15}}{27^{2}\times 9^{-3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$B=\frac{64x^{16}\times \frac{1}{8}x^{-15}}{27^{2}\times 9^{-3}}$$

Multiply 64 and \frac{1}{8} to get 8.

$$B=\frac{8x^{16}x^{-15}}{27^{2}\times 9^{-3}}$$

To multiply powers of the same base, add their exponents. Add 16 and -15 to get 1.

$$B=\frac{8x^{1}}{27^{2}\times 9^{-3}}$$

Calculate 27 to the power of 2 and get 729.

$$B=\frac{8x^{1}}{729\times 9^{-3}}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$B=\frac{8x^{1}}{729\times \frac{1}{729}}$$

Multiply 729 and \frac{1}{729} to get 1.

$$B=\frac{8x^{1}}{1}$$

Anything divided by one gives itself.

$$B=8x^{1}$$

Calculate x to the power of 1 and get x.

$$B=8x$$

Solve for x

$$x=\frac{B}{8}$$

$$B\neq 0$$

Steps for Solving Linear Equation

Calculate 3 to the power of 3 and get 27.

$$B=\frac{\left(\frac{8x^{8}}{27}\right)^{2}}{\left(\frac{3^{2}}{2x^{5}}\right)^{-3}}$$

To raise \frac{8x^{8}}{27} to a power, raise both numerator and denominator to the power and then divide.

$$B=\frac{\frac{\left(8x^{8}\right)^{2}}{27^{2}}}{\left(\frac{3^{2}}{2x^{5}}\right)^{-3}}$$

Calculate 3 to the power of 2 and get 9.

$$B=\frac{\frac{\left(8x^{8}\right)^{2}}{27^{2}}}{\left(\frac{9}{2x^{5}}\right)^{-3}}$$

To raise \frac{9}{2x^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$B=\frac{\frac{\left(8x^{8}\right)^{2}}{27^{2}}}{\frac{9^{-3}}{\left(2x^{5}\right)^{-3}}}$$

Divide \frac{\left(8x^{8}\right)^{2}}{27^{2}} by \frac{9^{-3}}{\left(2x^{5}\right)^{-3}} by multiplying \frac{\left(8x^{8}\right)^{2}}{27^{2}} by the reciprocal of \frac{9^{-3}}{\left(2x^{5}\right)^{-3}}.

$$B=\frac{\left(8x^{8}\right)^{2}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

Expand \left(8x^{8}\right)^{2}.

$$B=\frac{8^{2}\left(x^{8}\right)^{2}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$B=\frac{8^{2}x^{16}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

Calculate 8 to the power of 2 and get 64.

$$B=\frac{64x^{16}\times \left(2x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

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

$$B=\frac{64x^{16}\times 2^{-3}\left(x^{5}\right)^{-3}}{27^{2}\times 9^{-3}}$$

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

$$B=\frac{64x^{16}\times 2^{-3}x^{-15}}{27^{2}\times 9^{-3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$B=\frac{64x^{16}\times \frac{1}{8}x^{-15}}{27^{2}\times 9^{-3}}$$

Multiply 64 and \frac{1}{8} to get 8.

$$B=\frac{8x^{16}x^{-15}}{27^{2}\times 9^{-3}}$$

To multiply powers of the same base, add their exponents. Add 16 and -15 to get 1.

$$B=\frac{8x^{1}}{27^{2}\times 9^{-3}}$$

Calculate 27 to the power of 2 and get 729.

$$B=\frac{8x^{1}}{729\times 9^{-3}}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$B=\frac{8x^{1}}{729\times \frac{1}{729}}$$

Multiply 729 and \frac{1}{729} to get 1.

$$B=\frac{8x^{1}}{1}$$

Anything divided by one gives itself.

$$B=8x^{1}$$

Calculate x to the power of 1 and get x.

$$B=8x$$

Swap sides so that all variable terms are on the left hand side.

$$8x=B$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{B}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{B}{8}$$