Solve 6^-4*6^-9/6^-12*(3/5-2/5)text{H}4*(-1,25)+7-1,2^2

$$\frac { 6 ^ { - 4 } \cdot 6 ^ { - 9 } } { 6 ^ { - 12 } } \cdot ( \frac { 3 } { 5 } - \frac { 2 } { 5 } ) \text { H } 4 \cdot ( - 1,25 ) + 7 - 1,2 ^ { 2 }$$

Evaluate

$$-\frac{H}{6}+3$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -9 to get -13.

$$\frac{6^{-13}}{6^{-12}}\left(\frac{3}{5}-\frac{2}{5}\right)H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Rewrite 6^{-12} as 6\times 6^{-13}. Cancel out 6^{-13} in both numerator and denominator.

$$\frac{1}{6}\left(\frac{3}{5}-\frac{2}{5}\right)H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Subtract \frac{2}{5} from \frac{3}{5} to get \frac{1}{5}.

$$\frac{1}{6}\times \frac{1}{5}H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Multiply \frac{1}{6} and \frac{1}{5} to get \frac{1}{30}.

$$\frac{1}{30}H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Multiply \frac{1}{30} and 4 to get \frac{2}{15}.

$$\frac{2}{15}H\left(-1,25\right)+7-1\times 2^{2}$$

Multiply \frac{2}{15} and -1,25 to get -\frac{1}{6}.

$$-\frac{1}{6}H+7-1\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{1}{6}H+7-1\times 4$$

Multiply 1 and 4 to get 4.

$$-\frac{1}{6}H+7-4$$

Subtract 4 from 7 to get 3.

$$-\frac{1}{6}H+3$$

Expand

$$-\frac{H}{6}+3$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -9 to get -13.

$$\frac{6^{-13}}{6^{-12}}\left(\frac{3}{5}-\frac{2}{5}\right)H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Rewrite 6^{-12} as 6\times 6^{-13}. Cancel out 6^{-13} in both numerator and denominator.

$$\frac{1}{6}\left(\frac{3}{5}-\frac{2}{5}\right)H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Subtract \frac{2}{5} from \frac{3}{5} to get \frac{1}{5}.

$$\frac{1}{6}\times \frac{1}{5}H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Multiply \frac{1}{6} and \frac{1}{5} to get \frac{1}{30}.

$$\frac{1}{30}H\times 4\left(-1,25\right)+7-1\times 2^{2}$$

Multiply \frac{1}{30} and 4 to get \frac{2}{15}.

$$\frac{2}{15}H\left(-1,25\right)+7-1\times 2^{2}$$

Multiply \frac{2}{15} and -1,25 to get -\frac{1}{6}.

$$-\frac{1}{6}H+7-1\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{1}{6}H+7-1\times 4$$

Multiply 1 and 4 to get 4.

$$-\frac{1}{6}H+7-4$$

Subtract 4 from 7 to get 3.

$$-\frac{1}{6}H+3$$