Solve 2^101*3^101*(-1/6)^100

$$2 ^ { 101 } \times 3 ^ { 101 } \times ( - \frac { 1 } { 6 } ) ^ { 100 }$$

Evaluate

$$6$$

Solution Steps

Calculate 2 to the power of 101 and get 2535301200456458802993406410752.

$$2535301200456458802993406410752\times 3^{101}\left(-\frac{1}{6}\right)^{100}$$

Calculate 3 to the power of 101 and get 1546132562196033993109383389296863818106322566003.

$$2535301200456458802993406410752\times 1546132562196033993109383389296863818106322566003\left(-\frac{1}{6}\right)^{100}$$

Multiply 2535301200456458802993406410752 and 1546132562196033993109383389296863818106322566003 to get 3919911741000425436580141602948346923222862262837729229258431798216982848864256.

$$3919911741000425436580141602948346923222862262837729229258431798216982848864256\left(-\frac{1}{6}\right)^{100}$$

Calculate -\frac{1}{6} to the power of 100 and get \frac{1}{653318623500070906096690267158057820537143710472954871543071966369497141477376}.

$$3919911741000425436580141602948346923222862262837729229258431798216982848864256\times \frac{1}{653318623500070906096690267158057820537143710472954871543071966369497141477376}$$

Multiply 3919911741000425436580141602948346923222862262837729229258431798216982848864256 and \frac{1}{653318623500070906096690267158057820537143710472954871543071966369497141477376} to get \frac{3919911741000425436580141602948346923222862262837729229258431798216982848864256}{653318623500070906096690267158057820537143710472954871543071966369497141477376}.

$$\frac{3919911741000425436580141602948346923222862262837729229258431798216982848864256}{653318623500070906096690267158057820537143710472954871543071966369497141477376}$$

Divide 3919911741000425436580141602948346923222862262837729229258431798216982848864256 by 653318623500070906096690267158057820537143710472954871543071966369497141477376 to get 6.

$$6$$

Factor

$$2\times 3$$