Solve (31)(3^{2})^3*(2/3)^0*(1/6)^0*3^-2

$$( 31 ) ( 3 ^ { 2 } ) ^ { 3 } \times ( \frac { 2 } { 3 } ) ^ { 0 } \times ( \frac { 1 } { 6 } ) ^ { 0 } \times 3 ^ { - 2 }$$

Evaluate

$$2511$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$31\times 3^{6}\times \left(\frac{2}{3}\right)^{0}\times \left(\frac{1}{6}\right)^{0}\times 3^{-2}$$

To multiply powers of the same base, add their exponents. Add 6 and -2 to get 4.

$$31\times 3^{4}\times \left(\frac{2}{3}\right)^{0}\times \left(\frac{1}{6}\right)^{0}$$

Calculate 3 to the power of 4 and get 81.

$$31\times 81\times \left(\frac{2}{3}\right)^{0}\times \left(\frac{1}{6}\right)^{0}$$

Multiply 31 and 81 to get 2511.

$$2511\times \left(\frac{2}{3}\right)^{0}\times \left(\frac{1}{6}\right)^{0}$$

Calculate \frac{2}{3} to the power of 0 and get 1.

$$2511\times 1\times \left(\frac{1}{6}\right)^{0}$$

Multiply 2511 and 1 to get 2511.

$$2511\times \left(\frac{1}{6}\right)^{0}$$

Calculate \frac{1}{6} to the power of 0 and get 1.

$$2511\times 1$$

Multiply 2511 and 1 to get 2511.

$$2511$$

Factor

$$3^{4}\times 31$$