Solve frac{2(3a^{7})^{2}*ab^-7}{3c^-1*4a^10b^9}

$$\frac { 2 ( 3 a ^ { 7 } ) ^ { 2 } \cdot a b ^ { - 7 } } { 3 c ^ { - 1 } \cdot 4 a ^ { 10 } b ^ { 9 } }$$

Evaluate

$$\frac{3ca^{5}}{2b^{16}}$$

Solution Steps

Cancel out 2a in both numerator and denominator.

$$\frac{b^{-7}\times \left(3a^{7}\right)^{2}}{2\times 3\times \frac{1}{c}a^{9}b^{9}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(3a^{7}\right)^{2}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

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

$$\frac{3^{2}\left(a^{7}\right)^{2}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{3^{2}a^{14}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9a^{14}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

Multiply 2 and 3 to get 6.

$$\frac{9a^{14}}{6\times \frac{1}{c}a^{9}b^{16}}$$

Express 6\times \frac{1}{c} as a single fraction.

$$\frac{9a^{14}}{\frac{6}{c}a^{9}b^{16}}$$

Express \frac{6}{c}a^{9} as a single fraction.

$$\frac{9a^{14}}{\frac{6a^{9}}{c}b^{16}}$$

Express \frac{6a^{9}}{c}b^{16} as a single fraction.

$$\frac{9a^{14}}{\frac{6a^{9}b^{16}}{c}}$$

Divide 9a^{14} by \frac{6a^{9}b^{16}}{c} by multiplying 9a^{14} by the reciprocal of \frac{6a^{9}b^{16}}{c}.

$$\frac{9a^{14}c}{6a^{9}b^{16}}$$

Cancel out 3a^{9} in both numerator and denominator.

$$\frac{3ca^{5}}{2b^{16}}$$

Expand

$$\frac{3ca^{5}}{2b^{16}}$$

Solution Steps

Cancel out 2a in both numerator and denominator.

$$\frac{b^{-7}\times \left(3a^{7}\right)^{2}}{2\times 3\times \frac{1}{c}a^{9}b^{9}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(3a^{7}\right)^{2}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

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

$$\frac{3^{2}\left(a^{7}\right)^{2}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{3^{2}a^{14}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9a^{14}}{2\times 3\times \frac{1}{c}a^{9}b^{16}}$$

Multiply 2 and 3 to get 6.

$$\frac{9a^{14}}{6\times \frac{1}{c}a^{9}b^{16}}$$

Express 6\times \frac{1}{c} as a single fraction.

$$\frac{9a^{14}}{\frac{6}{c}a^{9}b^{16}}$$

Express \frac{6}{c}a^{9} as a single fraction.

$$\frac{9a^{14}}{\frac{6a^{9}}{c}b^{16}}$$

Express \frac{6a^{9}}{c}b^{16} as a single fraction.

$$\frac{9a^{14}}{\frac{6a^{9}b^{16}}{c}}$$

Divide 9a^{14} by \frac{6a^{9}b^{16}}{c} by multiplying 9a^{14} by the reciprocal of \frac{6a^{9}b^{16}}{c}.

$$\frac{9a^{14}c}{6a^{9}b^{16}}$$

Cancel out 3a^{9} in both numerator and denominator.

$$\frac{3ca^{5}}{2b^{16}}$$