Solve frac{(7a^{5}b^{8})(7a^{2}b^{3})^3}{(7^4a^6a^9)}

$$\frac { ( 7 a ^ { 5 } b ^ { 8 } ) ( 7 a ^ { 2 } b ^ { 3 } ) ^ { 3 } } { ( 7 ^ { 4 } a ^ { 6 } a ^ { 9 } ) }$$

Evaluate

$$\frac{b^{17}}{a^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{7a^{5}b^{8}\times \left(7a^{2}b^{3}\right)^{3}}{7^{4}a^{15}}$$

Cancel out 7a^{5} in both numerator and denominator.

$$\frac{b^{8}\times \left(7a^{2}b^{3}\right)^{3}}{7^{3}a^{10}}$$

Expand \left(7a^{2}b^{3}\right)^{3}.

$$\frac{b^{8}\times 7^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}}{7^{3}a^{10}}$$

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

$$\frac{b^{8}\times 7^{3}a^{6}\left(b^{3}\right)^{3}}{7^{3}a^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{b^{8}\times 7^{3}a^{6}b^{9}}{7^{3}a^{10}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{b^{8}\times 343a^{6}b^{9}}{7^{3}a^{10}}$$

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$\frac{b^{17}\times 343a^{6}}{7^{3}a^{10}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{b^{17}\times 343a^{6}}{343a^{10}}$$

Cancel out 343a^{6} in both numerator and denominator.

$$\frac{b^{17}}{a^{4}}$$

Expand

$$\frac{b^{17}}{a^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{7a^{5}b^{8}\times \left(7a^{2}b^{3}\right)^{3}}{7^{4}a^{15}}$$

Cancel out 7a^{5} in both numerator and denominator.

$$\frac{b^{8}\times \left(7a^{2}b^{3}\right)^{3}}{7^{3}a^{10}}$$

Expand \left(7a^{2}b^{3}\right)^{3}.

$$\frac{b^{8}\times 7^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}}{7^{3}a^{10}}$$

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

$$\frac{b^{8}\times 7^{3}a^{6}\left(b^{3}\right)^{3}}{7^{3}a^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{b^{8}\times 7^{3}a^{6}b^{9}}{7^{3}a^{10}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{b^{8}\times 343a^{6}b^{9}}{7^{3}a^{10}}$$

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$\frac{b^{17}\times 343a^{6}}{7^{3}a^{10}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{b^{17}\times 343a^{6}}{343a^{10}}$$

Cancel out 343a^{6} in both numerator and denominator.

$$\frac{b^{17}}{a^{4}}$$