Solve frac{6^{2}*6^3}{6^4}+2^-2+sqrt[15]{(-1/8)^5}=

$$\frac { 6 ^ { 2 } \cdot 6 ^ { 3 } } { 6 ^ { 4 } } + 2 ^ { - 2 } + \sqrt[ 15 ] { ( - \frac { 1 } { 8 } ) ^ { 5 } } =$$

Evaluate

$$\frac{23}{4}=5.75$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{6^{5}}{6^{4}}+2^{-2}+\sqrt[15]{\left(-\frac{1}{8}\right)^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$6^{1}+2^{-2}+\sqrt[15]{\left(-\frac{1}{8}\right)^{5}}$$

Calculate 6 to the power of 1 and get 6.

$$6+2^{-2}+\sqrt[15]{\left(-\frac{1}{8}\right)^{5}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$6+\frac{1}{4}+\sqrt[15]{\left(-\frac{1}{8}\right)^{5}}$$

Add 6 and \frac{1}{4} to get \frac{25}{4}.

$$\frac{25}{4}+\sqrt[15]{\left(-\frac{1}{8}\right)^{5}}$$

Calculate -\frac{1}{8} to the power of 5 and get -\frac{1}{32768}.

$$\frac{25}{4}+\sqrt[15]{-\frac{1}{32768}}$$

Calculate \sqrt[15]{-\frac{1}{32768}} and get -\frac{1}{2}.

$$\frac{25}{4}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{25}{4} to get \frac{23}{4}.

$$\frac{23}{4}$$

Factor

$$\frac{23}{2 ^ {2}} = 5\frac{3}{4} = 5.75$$