Solve frac{(-4a^{2}b)^{2}}{21x^3y^2}*3x^2y/(2a)^2b=

$$\frac { ( - 4 a ^ { 2 } b ) ^ { 2 } } { 21 x ^ { 3 } y ^ { 2 } } \times \frac { 3 x ^ { 2 } y } { ( 2 a ) ^ { 2 } b } =$$

Evaluate

$$\frac{4ba^{2}}{7xy}$$

Solution Steps

Expand \left(-4a^{2}b\right)^{2}.

$$\frac{\left(-4\right)^{2}\left(a^{2}\right)^{2}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{\left(2a\right)^{2}b}$$

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

$$\frac{\left(-4\right)^{2}a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{\left(2a\right)^{2}b}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{16a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{\left(2a\right)^{2}b}$$

Expand \left(2a\right)^{2}.

$$\frac{16a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{2^{2}a^{2}b}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{4a^{2}b}$$

Multiply \frac{16a^{4}b^{2}}{21x^{3}y^{2}} times \frac{3x^{2}y}{4a^{2}b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16a^{4}b^{2}\times 3x^{2}y}{21x^{3}y^{2}\times 4a^{2}b}$$

Cancel out 3\times 4bya^{2}x^{2} in both numerator and denominator.

$$\frac{4ba^{2}}{7xy}$$

Expand

$$\frac{4ba^{2}}{7xy}$$

Solution Steps

Expand \left(-4a^{2}b\right)^{2}.

$$\frac{\left(-4\right)^{2}\left(a^{2}\right)^{2}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{\left(2a\right)^{2}b}$$

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

$$\frac{\left(-4\right)^{2}a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{\left(2a\right)^{2}b}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{16a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{\left(2a\right)^{2}b}$$

Expand \left(2a\right)^{2}.

$$\frac{16a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{2^{2}a^{2}b}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16a^{4}b^{2}}{21x^{3}y^{2}}\times \frac{3x^{2}y}{4a^{2}b}$$

Multiply \frac{16a^{4}b^{2}}{21x^{3}y^{2}} times \frac{3x^{2}y}{4a^{2}b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16a^{4}b^{2}\times 3x^{2}y}{21x^{3}y^{2}\times 4a^{2}b}$$

Cancel out 3\times 4bya^{2}x^{2} in both numerator and denominator.

$$\frac{4ba^{2}}{7xy}$$