Solve frac{a^{6}b*a^{8}b^5}{(a^3b^8)^2}

$$\frac { a ^ { 6 } b \cdot a ^ { 8 } b ^ { 5 } } { ( a ^ { 3 } b ^ { 8 } ) ^ { 2 } }$$

Evaluate

$$\frac{a^{8}}{b^{10}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{a^{14}bb^{5}}{\left(a^{3}b^{8}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{a^{14}b^{6}}{\left(a^{3}b^{8}\right)^{2}}$$

Expand \left(a^{3}b^{8}\right)^{2}.

$$\frac{a^{14}b^{6}}{\left(a^{3}\right)^{2}\left(b^{8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{a^{14}b^{6}}{a^{6}\left(b^{8}\right)^{2}}$$

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

$$\frac{a^{14}b^{6}}{a^{6}b^{16}}$$

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

$$\frac{a^{8}}{b^{10}}$$

Expand

$$\frac{a^{8}}{b^{10}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 8 to get 14.

$$\frac{a^{14}bb^{5}}{\left(a^{3}b^{8}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{a^{14}b^{6}}{\left(a^{3}b^{8}\right)^{2}}$$

Expand \left(a^{3}b^{8}\right)^{2}.

$$\frac{a^{14}b^{6}}{\left(a^{3}\right)^{2}\left(b^{8}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{a^{14}b^{6}}{a^{6}\left(b^{8}\right)^{2}}$$

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

$$\frac{a^{14}b^{6}}{a^{6}b^{16}}$$

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

$$\frac{a^{8}}{b^{10}}$$