Solve frac{a^{4}*(ab^2)^2}{(a^8b)^2}

$$\frac { a ^ { 4 } \times ( a b ^ { 2 } ) ^ { 2 } } { ( a ^ { 8 } b ) ^ { 2 } }$$

Evaluate

$$\frac{b^{2}}{a^{10}}$$

Solution Steps

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

$$\frac{a^{4}a^{2}\left(b^{2}\right)^{2}}{\left(a^{8}b\right)^{2}}$$

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

$$\frac{a^{4}a^{2}b^{4}}{\left(a^{8}b\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{a^{6}b^{4}}{\left(a^{8}b\right)^{2}}$$

Expand \left(a^{8}b\right)^{2}.

$$\frac{a^{6}b^{4}}{\left(a^{8}\right)^{2}b^{2}}$$

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

$$\frac{a^{6}b^{4}}{a^{16}b^{2}}$$

Cancel out b^{2}a^{6} in both numerator and denominator.

$$\frac{b^{2}}{a^{10}}$$

Expand

$$\frac{b^{2}}{a^{10}}$$

Solution Steps

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

$$\frac{a^{4}a^{2}\left(b^{2}\right)^{2}}{\left(a^{8}b\right)^{2}}$$

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

$$\frac{a^{4}a^{2}b^{4}}{\left(a^{8}b\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{a^{6}b^{4}}{\left(a^{8}b\right)^{2}}$$

Expand \left(a^{8}b\right)^{2}.

$$\frac{a^{6}b^{4}}{\left(a^{8}\right)^{2}b^{2}}$$

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

$$\frac{a^{6}b^{4}}{a^{16}b^{2}}$$

Cancel out b^{2}a^{6} in both numerator and denominator.

$$\frac{b^{2}}{a^{10}}$$