Solve (frac{2m^{-3}w^{4}}{m^{5}})^{2}*(3mw^5/m^2)(4w^-8/m^-7)

$$( \frac { 2 m ^ { - 3 } w ^ { 4 } } { m ^ { 5 } } ) ^ { 2 } \cdot ( \frac { 3 m w ^ { 5 } } { m ^ { 2 } } ) ( \frac { 4 w ^ { - 8 } } { m ^ { - 7 } } )$$

Evaluate

$$\frac{48w^{5}}{m^{10}}$$

Solution Steps

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

$$\left(\frac{2w^{4}}{m^{8}}\right)^{2}\times \frac{3mw^{5}}{m^{2}}\times \frac{4w^{-8}}{m^{-7}}$$

To raise \frac{2w^{4}}{m^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2w^{4}\right)^{2}}{\left(m^{8}\right)^{2}}\times \frac{3mw^{5}}{m^{2}}\times \frac{4w^{-8}}{m^{-7}}$$

Cancel out m in both numerator and denominator.

$$\frac{\left(2w^{4}\right)^{2}}{\left(m^{8}\right)^{2}}\times \frac{3w^{5}}{m}\times \frac{4w^{-8}}{m^{-7}}$$

Multiply \frac{\left(2w^{4}\right)^{2}}{\left(m^{8}\right)^{2}} times \frac{3w^{5}}{m} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{5}}{\left(m^{8}\right)^{2}m}\times \frac{4w^{-8}}{m^{-7}}$$

Multiply \frac{\left(2w^{4}\right)^{2}\times 3w^{5}}{\left(m^{8}\right)^{2}m} times \frac{4w^{-8}}{m^{-7}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{5}\times 4w^{-8}}{\left(m^{8}\right)^{2}mm^{-7}}$$

To multiply powers of the same base, add their exponents. Add 5 and -8 to get -3.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{\left(m^{8}\right)^{2}mm^{-7}}$$

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

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{16}mm^{-7}}$$

To multiply powers of the same base, add their exponents. Add 16 and 1 to get 17.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{17}m^{-7}}$$

To multiply powers of the same base, add their exponents. Add 17 and -7 to get 10.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{10}}$$

Expand \left(2w^{4}\right)^{2}.

$$\frac{2^{2}\left(w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{10}}$$

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

$$\frac{2^{2}w^{8}\times 3w^{-3}\times 4}{m^{10}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4w^{8}\times 3w^{-3}\times 4}{m^{10}}$$

Multiply 4 and 3 to get 12.

$$\frac{12w^{8}w^{-3}\times 4}{m^{10}}$$

To multiply powers of the same base, add their exponents. Add 8 and -3 to get 5.

$$\frac{12w^{5}\times 4}{m^{10}}$$

Multiply 12 and 4 to get 48.

$$\frac{48w^{5}}{m^{10}}$$

Expand

$$\frac{48w^{5}}{m^{10}}$$

Solution Steps

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

$$\left(\frac{2w^{4}}{m^{8}}\right)^{2}\times \frac{3mw^{5}}{m^{2}}\times \frac{4w^{-8}}{m^{-7}}$$

To raise \frac{2w^{4}}{m^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2w^{4}\right)^{2}}{\left(m^{8}\right)^{2}}\times \frac{3mw^{5}}{m^{2}}\times \frac{4w^{-8}}{m^{-7}}$$

Cancel out m in both numerator and denominator.

$$\frac{\left(2w^{4}\right)^{2}}{\left(m^{8}\right)^{2}}\times \frac{3w^{5}}{m}\times \frac{4w^{-8}}{m^{-7}}$$

Multiply \frac{\left(2w^{4}\right)^{2}}{\left(m^{8}\right)^{2}} times \frac{3w^{5}}{m} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{5}}{\left(m^{8}\right)^{2}m}\times \frac{4w^{-8}}{m^{-7}}$$

Multiply \frac{\left(2w^{4}\right)^{2}\times 3w^{5}}{\left(m^{8}\right)^{2}m} times \frac{4w^{-8}}{m^{-7}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{5}\times 4w^{-8}}{\left(m^{8}\right)^{2}mm^{-7}}$$

To multiply powers of the same base, add their exponents. Add 5 and -8 to get -3.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{\left(m^{8}\right)^{2}mm^{-7}}$$

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

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{16}mm^{-7}}$$

To multiply powers of the same base, add their exponents. Add 16 and 1 to get 17.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{17}m^{-7}}$$

To multiply powers of the same base, add their exponents. Add 17 and -7 to get 10.

$$\frac{\left(2w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{10}}$$

Expand \left(2w^{4}\right)^{2}.

$$\frac{2^{2}\left(w^{4}\right)^{2}\times 3w^{-3}\times 4}{m^{10}}$$

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

$$\frac{2^{2}w^{8}\times 3w^{-3}\times 4}{m^{10}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4w^{8}\times 3w^{-3}\times 4}{m^{10}}$$

Multiply 4 and 3 to get 12.

$$\frac{12w^{8}w^{-3}\times 4}{m^{10}}$$

To multiply powers of the same base, add their exponents. Add 8 and -3 to get 5.

$$\frac{12w^{5}\times 4}{m^{10}}$$

Multiply 12 and 4 to get 48.

$$\frac{48w^{5}}{m^{10}}$$