Solve (frac{7a^{2}b^3}{a^3b^5})^2

$$( \frac { 7 a ^ { 2 } b ^ { 3 } } { a ^ { 3 } b ^ { 5 } } ) ^ { 2 }$$

Evaluate

$$\frac{49}{a^{2}b^{4}}$$

Solution Steps

Cancel out a^{2}b^{3} in both numerator and denominator.

$$\left(\frac{7}{ab^{2}}\right)^{2}$$

To raise \frac{7}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{7^{2}}{\left(ab^{2}\right)^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49}{\left(ab^{2}\right)^{2}}$$

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

$$\frac{49}{a^{2}\left(b^{2}\right)^{2}}$$

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

$$\frac{49}{a^{2}b^{4}}$$

Expand

$$\frac{49}{a^{2}b^{4}}$$

Solution Steps

Cancel out a^{2}b^{3} in both numerator and denominator.

$$\left(\frac{7}{ab^{2}}\right)^{2}$$

To raise \frac{7}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{7^{2}}{\left(ab^{2}\right)^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49}{\left(ab^{2}\right)^{2}}$$

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

$$\frac{49}{a^{2}\left(b^{2}\right)^{2}}$$

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

$$\frac{49}{a^{2}b^{4}}$$