Solve (frac{7^frac{3{4}}*2^frac{3{4}}}{2^-frac{1{4}}*14})^-4

$$( \frac { 7 ^ { \frac { 3 } { 4 } } \cdot 2 ^ { \frac { 3 } { 4 } } } { 2 ^ { - \frac { 1 } { 4 } } \cdot 14 } ) ^ { - 4 }$$

Evaluate

$$7$$

Solution Steps

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

$$\left(\frac{2^{1}\times 7^{\frac{3}{4}}}{14}\right)^{-4}$$

Calculate 2 to the power of 1 and get 2.

$$\left(\frac{2\times 7^{\frac{3}{4}}}{14}\right)^{-4}$$

Divide 2\times 7^{\frac{3}{4}} by 14 to get \frac{1}{7}\times 7^{\frac{3}{4}}.

$$\left(\frac{1}{7}\times 7^{\frac{3}{4}}\right)^{-4}$$

Expand \left(\frac{1}{7}\times 7^{\frac{3}{4}}\right)^{-4}.

$$\left(\frac{1}{7}\right)^{-4}\times \left(7^{\frac{3}{4}}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and -4 to get -3.

$$\left(\frac{1}{7}\right)^{-4}\times 7^{-3}$$

Calculate \frac{1}{7} to the power of -4 and get 2401.

$$2401\times 7^{-3}$$

Calculate 7 to the power of -3 and get \frac{1}{343}.

$$2401\times \frac{1}{343}$$

Multiply 2401 and \frac{1}{343} to get 7.

$$7$$

Factor

$$7$$