Solve frac{36x^{4}y^{21}(2w^{5})^2}{12x^-3y^5w^12}

$$\frac { 36 x ^ { 4 } y ^ { 21 } ( 2 w ^ { 5 } ) ^ { 2 } } { 12 x ^ { - 3 } y ^ { 5 } w ^ { 12 } }$$

Evaluate

$$\frac{12x^{7}y^{16}}{w^{2}}$$

Solution Steps

Cancel out 12y^{5} in both numerator and denominator.

$$\frac{3x^{4}\times \left(2w^{5}\right)^{2}y^{16}}{x^{-3}w^{12}}$$

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

$$\frac{3x^{7}\times \left(2w^{5}\right)^{2}y^{16}}{w^{12}}$$

Expand \left(2w^{5}\right)^{2}.

$$\frac{3x^{7}\times 2^{2}\left(w^{5}\right)^{2}y^{16}}{w^{12}}$$

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

$$\frac{3x^{7}\times 2^{2}w^{10}y^{16}}{w^{12}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3x^{7}\times 4w^{10}y^{16}}{w^{12}}$$

Multiply 3 and 4 to get 12.

$$\frac{12x^{7}w^{10}y^{16}}{w^{12}}$$

Cancel out w^{10} in both numerator and denominator.

$$\frac{12x^{7}y^{16}}{w^{2}}$$

Expand

$$\frac{12x^{7}y^{16}}{w^{2}}$$

Solution Steps

Cancel out 12y^{5} in both numerator and denominator.

$$\frac{3x^{4}\times \left(2w^{5}\right)^{2}y^{16}}{x^{-3}w^{12}}$$

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

$$\frac{3x^{7}\times \left(2w^{5}\right)^{2}y^{16}}{w^{12}}$$

Expand \left(2w^{5}\right)^{2}.

$$\frac{3x^{7}\times 2^{2}\left(w^{5}\right)^{2}y^{16}}{w^{12}}$$

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

$$\frac{3x^{7}\times 2^{2}w^{10}y^{16}}{w^{12}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3x^{7}\times 4w^{10}y^{16}}{w^{12}}$$

Multiply 3 and 4 to get 12.

$$\frac{12x^{7}w^{10}y^{16}}{w^{12}}$$

Cancel out w^{10} in both numerator and denominator.

$$\frac{12x^{7}y^{16}}{w^{2}}$$