Solve I(3^{7}:3^{5}+2^{6}:2^{4}+6^{6}:6^{5}+2^{8}:2^7):3]*(2^8*2^2:2^7)

$$I ( 3 ^ { 7 } : 3 ^ { 5 } + 2 ^ { 6 } : 2 ^ { 4 } + 6 ^ { 6 } : 6 ^ { 5 } + 2 ^ { 8 } : 2 ^ { 7 } ) : 3 ] \times ( 2 ^ { 8 } \times 2 ^ { 2 } : 2 ^ { 7 } )$$

Evaluate

$$7I$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$\frac{I\left(3^{2}+\frac{2^{6}}{2^{4}}+\frac{6^{6}}{6^{5}}+\frac{2^{8}}{2^{7}}\right)}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$\frac{I\left(3^{2}+2^{2}+\frac{6^{6}}{6^{5}}+\frac{2^{8}}{2^{7}}\right)}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$\frac{I\left(3^{2}+2^{2}+6^{1}+\frac{2^{8}}{2^{7}}\right)}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 8 to get 1.

$$\frac{I\left(3^{2}+2^{2}+6^{1}+2^{1}\right)}{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{I\left(9+2^{2}+6^{1}+2^{1}\right)}{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{I\left(9+4+6^{1}+2^{1}\right)}{3}$$

Add 9 and 4 to get 13.

$$\frac{I\left(13+6^{1}+2^{1}\right)}{3}$$

Calculate 6 to the power of 1 and get 6.

$$\frac{I\left(13+6+2^{1}\right)}{3}$$

Add 13 and 6 to get 19.

$$\frac{I\left(19+2^{1}\right)}{3}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{I\left(19+2\right)}{3}$$

Add 19 and 2 to get 21.

$$\frac{I\times 21}{3}$$

Divide I\times 21 by 3 to get I\times 7.

$$I\times 7$$

Expand

$$7I$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$\frac{I\left(3^{2}+\frac{2^{6}}{2^{4}}+\frac{6^{6}}{6^{5}}+\frac{2^{8}}{2^{7}}\right)}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$\frac{I\left(3^{2}+2^{2}+\frac{6^{6}}{6^{5}}+\frac{2^{8}}{2^{7}}\right)}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$\frac{I\left(3^{2}+2^{2}+6^{1}+\frac{2^{8}}{2^{7}}\right)}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 8 to get 1.

$$\frac{I\left(3^{2}+2^{2}+6^{1}+2^{1}\right)}{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{I\left(9+2^{2}+6^{1}+2^{1}\right)}{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{I\left(9+4+6^{1}+2^{1}\right)}{3}$$

Add 9 and 4 to get 13.

$$\frac{I\left(13+6^{1}+2^{1}\right)}{3}$$

Calculate 6 to the power of 1 and get 6.

$$\frac{I\left(13+6+2^{1}\right)}{3}$$

Add 13 and 6 to get 19.

$$\frac{I\left(19+2^{1}\right)}{3}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{I\left(19+2\right)}{3}$$

Add 19 and 2 to get 21.

$$\frac{I\times 21}{3}$$

Divide I\times 21 by 3 to get I\times 7.

$$I\times 7$$