For example, you can use this method to multiply 52×53{\displaystyle 5^{2}\times 5^{3}}, because they both have the same base (5). On the other hand, you cannot use this method to multiply 52×23{\displaystyle 5^{2}\times 2^{3}}, because they have different bases (5 and 2).
For example, if you are multiplying 52×53{\displaystyle 5^{2}\times 5^{3}}, you would keep the base of 5, and add the exponents together:52×53{\displaystyle 5^{2}\times 5^{3}}=52+3{\displaystyle =5^{2+3}}=55{\displaystyle =5^{5}}
For example 55=5×5×5×5×5{\displaystyle 5^{5}=5\times 5\times 5\times 5\times 5}55=3,125{\displaystyle 5^{5}=3,125}So, 52×53=3,125{\displaystyle 5^{2}\times 5^{3}=3,125}
For example, if you are multiplying 23×45{\displaystyle 2^{3}\times 4^{5}}, you should note that they do not have the same base. So, you will first calculate 23=2×2×2=8{\displaystyle 2^{3}=2\times 2\times 2=8}.
For example, 45=4×4×4×4×4=1024{\displaystyle 4^{5}=4\times 4\times 4\times 4\times 4=1024}
For example: 8×1024=8192. {\displaystyle 8\times 1024=8192. } So, 23×45=8,192{\displaystyle 2^{3}\times 4^{5}=8,192}.
For example, if multiplying (2x3y5)(8xy4){\displaystyle (2x^{3}y^{5})(8xy^{4})}, you would first calculate ((2)x3y5)((8)xy4)=16(x3y5)(xy4){\displaystyle ((2)x^{3}y^{5})((8)xy^{4})=16(x^{3}y^{5})(xy^{4})}.
For example:16(x3y5)(xy4)=16(x3)y5(x)y4=16(x3+1)y5y4=16(x4)y5y4{\displaystyle 16(x^{3}y^{5})(xy^{4})=16(x^{3})y^{5}(x)y^{4}=16(x^{3+1})y^{5}y^{4}=16(x^{4})y^{5}y^{4}}
For example: 16(x4)y5y4=16x4y5+4=16x4y9{\displaystyle 16(x^{4})y^{5}y^{4}=16x^{4}y^{5+4}=16x^{4}y^{9}}
