Solve (frac{-7a^{2}b^-3}{5a^-4b^3})^2

$$( \frac { - 7 a ^ { 2 } b ^ { - 3 } } { 5 a ^ { - 4 } b ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{49\times \left(\frac{a}{b}\right)^{12}}{25}$$

Solution Steps

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

$$\left(\frac{-7b^{-3}a^{6}}{5b^{3}}\right)^{2}$$

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

$$\left(\frac{-7a^{6}}{5b^{6}}\right)^{2}$$

To raise \frac{-7a^{6}}{5b^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-7a^{6}\right)^{2}}{\left(5b^{6}\right)^{2}}$$

Expand \left(-7a^{6}\right)^{2}.

$$\frac{\left(-7\right)^{2}\left(a^{6}\right)^{2}}{\left(5b^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{\left(-7\right)^{2}a^{12}}{\left(5b^{6}\right)^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{49a^{12}}{\left(5b^{6}\right)^{2}}$$

Expand \left(5b^{6}\right)^{2}.

$$\frac{49a^{12}}{5^{2}\left(b^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{49a^{12}}{5^{2}b^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{49a^{12}}{25b^{12}}$$

Expand

$$\frac{49\times \left(\frac{a}{b}\right)^{12}}{25}$$

Solution Steps

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

$$\left(\frac{-7b^{-3}a^{6}}{5b^{3}}\right)^{2}$$

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

$$\left(\frac{-7a^{6}}{5b^{6}}\right)^{2}$$

To raise \frac{-7a^{6}}{5b^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-7a^{6}\right)^{2}}{\left(5b^{6}\right)^{2}}$$

Expand \left(-7a^{6}\right)^{2}.

$$\frac{\left(-7\right)^{2}\left(a^{6}\right)^{2}}{\left(5b^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{\left(-7\right)^{2}a^{12}}{\left(5b^{6}\right)^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{49a^{12}}{\left(5b^{6}\right)^{2}}$$

Expand \left(5b^{6}\right)^{2}.

$$\frac{49a^{12}}{5^{2}\left(b^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{49a^{12}}{5^{2}b^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{49a^{12}}{25b^{12}}$$