Solve (8mn^2/m^-3n)^-2*(n^5z/4m)

$$( \frac { 8 m n ^ { 2 } } { m ^ { - 3 } n } ) ^ { - 2 } \cdot ( \frac { n ^ { 5 } z } { 4 m } )$$

Evaluate

$$\frac{zn^{3}}{256m^{9}}$$

Solution Steps

Cancel out n in both numerator and denominator.

$$\left(\frac{8mn}{m^{-3}}\right)^{-2}\times \frac{n^{5}z}{4m}$$

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

$$\left(8nm^{4}\right)^{-2}\times \frac{n^{5}z}{4m}$$

Expand \left(8nm^{4}\right)^{-2}.

$$8^{-2}n^{-2}\left(m^{4}\right)^{-2}\times \frac{n^{5}z}{4m}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$8^{-2}n^{-2}m^{-8}\times \frac{n^{5}z}{4m}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{1}{64}n^{-2}m^{-8}\times \frac{n^{5}z}{4m}$$

Multiply \frac{1}{64} times \frac{n^{5}z}{4m} by multiplying numerator times numerator and denominator times denominator.

$$\frac{n^{5}z}{64\times 4m}n^{-2}m^{-8}$$

Multiply 64 and 4 to get 256.

$$\frac{n^{5}z}{256m}n^{-2}m^{-8}$$

Express \frac{n^{5}z}{256m}n^{-2} as a single fraction.

$$\frac{n^{5}zn^{-2}}{256m}m^{-8}$$

Express \frac{n^{5}zn^{-2}}{256m}m^{-8} as a single fraction.

$$\frac{n^{5}zn^{-2}m^{-8}}{256m}$$

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

$$\frac{n^{-2}zn^{5}}{256m^{9}}$$

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\frac{n^{3}z}{256m^{9}}$$

Expand

$$\frac{zn^{3}}{256m^{9}}$$

Solution Steps

Cancel out n in both numerator and denominator.

$$\left(\frac{8mn}{m^{-3}}\right)^{-2}\times \frac{n^{5}z}{4m}$$

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

$$\left(8nm^{4}\right)^{-2}\times \frac{n^{5}z}{4m}$$

Expand \left(8nm^{4}\right)^{-2}.

$$8^{-2}n^{-2}\left(m^{4}\right)^{-2}\times \frac{n^{5}z}{4m}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$8^{-2}n^{-2}m^{-8}\times \frac{n^{5}z}{4m}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{1}{64}n^{-2}m^{-8}\times \frac{n^{5}z}{4m}$$

Multiply \frac{1}{64} times \frac{n^{5}z}{4m} by multiplying numerator times numerator and denominator times denominator.

$$\frac{n^{5}z}{64\times 4m}n^{-2}m^{-8}$$

Multiply 64 and 4 to get 256.

$$\frac{n^{5}z}{256m}n^{-2}m^{-8}$$

Express \frac{n^{5}z}{256m}n^{-2} as a single fraction.

$$\frac{n^{5}zn^{-2}}{256m}m^{-8}$$

Express \frac{n^{5}zn^{-2}}{256m}m^{-8} as a single fraction.

$$\frac{n^{5}zn^{-2}m^{-8}}{256m}$$

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

$$\frac{n^{-2}zn^{5}}{256m^{9}}$$

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\frac{n^{3}z}{256m^{9}}$$