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10m^4* (2m^5)^6

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When solving a problem like this you must remember order of operations.  Most people remember PEMDAS (parenthesis, exponent, multiplication, division, addition, subtraction).  Because you have parenthesis you must do that operation first so we will look at (2m^5)^6.  The 6 gets distributed to both the 2 and the m inside the parenthesis.  2^6=64 and (m^5)^6=m^30.  Now we have 10m^4 * 64m^30.  The only operation you have now is multiplication.  Multiply the coefficients together, 10*64=640, and multiply the m's together. m^4 * m^30 = m^34, so the final answer is 640m^34  :)


Exponent Rules:

xm • xn = xm+n
xm / xn = xm-n
(xm)n = xmn