Solve (1/2)^{0}*[(1/2)^3]^-4:(1/3)^9*(1/3)^10=

$$( \frac { 1 } { 2 } ) ^ { 0 } \cdot [ ( \frac { 1 } { 2 } ) ^ { 3 } ] ^ { - 4 } : ( \frac { 1 } { 3 } ) ^ { 9 } \cdot ( \frac { 1 } { 3 } ) ^ { 10 } =$$

Evaluate

$$\frac{4096}{3}\approx 1365.333333333$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$\frac{\left(\frac{1}{2}\right)^{0}\times \left(\frac{1}{2}\right)^{-12}}{\left(\frac{1}{3}\right)^{9}}\times \left(\frac{1}{3}\right)^{10}$$

To multiply powers of the same base, add their exponents. Add 0 and -12 to get -12.

$$\frac{\left(\frac{1}{2}\right)^{-12}}{\left(\frac{1}{3}\right)^{9}}\times \left(\frac{1}{3}\right)^{10}$$

Calculate \frac{1}{2} to the power of -12 and get 4096.

$$\frac{4096}{\left(\frac{1}{3}\right)^{9}}\times \left(\frac{1}{3}\right)^{10}$$

Calculate \frac{1}{3} to the power of 9 and get \frac{1}{19683}.

$$\frac{4096}{\frac{1}{19683}}\times \left(\frac{1}{3}\right)^{10}$$

Divide 4096 by \frac{1}{19683} by multiplying 4096 by the reciprocal of \frac{1}{19683}.

$$4096\times 19683\times \left(\frac{1}{3}\right)^{10}$$

Multiply 4096 and 19683 to get 80621568.

$$80621568\times \left(\frac{1}{3}\right)^{10}$$

Calculate \frac{1}{3} to the power of 10 and get \frac{1}{59049}.

$$80621568\times \frac{1}{59049}$$

Multiply 80621568 and \frac{1}{59049} to get \frac{4096}{3}.

$$\frac{4096}{3}$$

Factor

$$\frac{2 ^ {12}}{3} = 1365\frac{1}{3} = 1365.3333333333333$$