Solve (2a^2/b)(a/b^2)^2

$$( \frac { 2 a ^ { 2 } } { b } ) ( \frac { a } { b ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{2a^{4}}{b^{5}}$$

Solution Steps

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

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

Multiply \frac{2a^{2}}{b} times \frac{a^{2}}{\left(b^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{2a^{4}}{b\left(b^{2}\right)^{2}}$$

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

$$\frac{2a^{4}}{bb^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{2a^{4}}{b^{5}}$$

Expand

$$\frac{2a^{4}}{b^{5}}$$

Solution Steps

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

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

Multiply \frac{2a^{2}}{b} times \frac{a^{2}}{\left(b^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{2a^{4}}{b\left(b^{2}\right)^{2}}$$

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

$$\frac{2a^{4}}{bb^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{2a^{4}}{b^{5}}$$