What Is the Way to Multiply Exponents With Different Bases?


Quick Answer

When multiplying exponents with different bases, multiply the bases first. For instance, when multiplying y^2 * z^2, the formula would change to (y * z)^2.

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Full Answer

An example of multiplying exponents with different bases is 3^2 * 4^2. Users should change the equation to read as (3 * 4)^2 which is equal to 12^2. To solve 12^2, users would multiply 12*12 which is equal to 144.

When multiplying numbers where both the base and exponents are different, such as 2^2 * 3^3, each exponents has to be calculated first. In this equation, users would first calculate each part of the equation separately, 2^2 = 4 and 3^3=9 and then multiply 4 by 9 which equals 36. So 2^2 * 3^3 = 36.

The process changes when two different negative exponents are involved as the exponents are added together. An instance of multiplying negative exponents is 2^-2 * 2^-3. The equation should be changed to 2^-(2+3) which equals 2^-5. Because the exponent is negative, the number changes to a fraction in order to make it positive. It would change to 1/2^5, then users would then take 1/2*2*2*2*2 which is equal to 1/32. Diving 1 by 33 gives the answer 0.03125, so 2^-2 * 2^-3 = 0.03125.

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