Solve (frac{6^{-3}y^4}{7x^2y^-7})^2

$$( \frac { 6 ^ { - 3 } y ^ { 4 } } { 7 x ^ { 2 } y ^ { - 7 } } ) ^ { 2 }$$

Evaluate

$$\frac{y^{22}}{2286144x^{4}}$$

Solution Steps

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

$$\left(\frac{6^{-3}y^{11}}{7x^{2}}\right)^{2}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\left(\frac{\frac{1}{216}y^{11}}{7x^{2}}\right)^{2}$$

To raise \frac{\frac{1}{216}y^{11}}{7x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\frac{1}{216}y^{11}\right)^{2}}{\left(7x^{2}\right)^{2}}$$

Expand \left(\frac{1}{216}y^{11}\right)^{2}.

$$\frac{\left(\frac{1}{216}\right)^{2}\left(y^{11}\right)^{2}}{\left(7x^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 2 to get 22.

$$\frac{\left(\frac{1}{216}\right)^{2}y^{22}}{\left(7x^{2}\right)^{2}}$$

Calculate \frac{1}{216} to the power of 2 and get \frac{1}{46656}.

$$\frac{\frac{1}{46656}y^{22}}{\left(7x^{2}\right)^{2}}$$

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

$$\frac{\frac{1}{46656}y^{22}}{7^{2}\left(x^{2}\right)^{2}}$$

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

$$\frac{\frac{1}{46656}y^{22}}{7^{2}x^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\frac{1}{46656}y^{22}}{49x^{4}}$$

Expand

$$\frac{y^{22}}{2286144x^{4}}$$

Solution Steps

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

$$\left(\frac{6^{-3}y^{11}}{7x^{2}}\right)^{2}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\left(\frac{\frac{1}{216}y^{11}}{7x^{2}}\right)^{2}$$

To raise \frac{\frac{1}{216}y^{11}}{7x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\frac{1}{216}y^{11}\right)^{2}}{\left(7x^{2}\right)^{2}}$$

Expand \left(\frac{1}{216}y^{11}\right)^{2}.

$$\frac{\left(\frac{1}{216}\right)^{2}\left(y^{11}\right)^{2}}{\left(7x^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 2 to get 22.

$$\frac{\left(\frac{1}{216}\right)^{2}y^{22}}{\left(7x^{2}\right)^{2}}$$

Calculate \frac{1}{216} to the power of 2 and get \frac{1}{46656}.

$$\frac{\frac{1}{46656}y^{22}}{\left(7x^{2}\right)^{2}}$$

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

$$\frac{\frac{1}{46656}y^{22}}{7^{2}\left(x^{2}\right)^{2}}$$

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

$$\frac{\frac{1}{46656}y^{22}}{7^{2}x^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\frac{1}{46656}y^{22}}{49x^{4}}$$