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Exercises: Power Laws

Simplify the following expressions with integer exponents as far as possible.

  1. (z2k5:z3):zk

  2. 903n23n

  3. [(x4)3]5:(x2)6 for x0

  4. (3a1)2k1(13a)2k+1 for a13

  5. (6a2b2cn+1d2n)3:[2(cd)nab1cnd2n3ab2]2 for a,b,c,d0

  6. x2a+5(y3)2b+5[(z)4]3b+3:x2a(yz)6b+10[(z)3]2b1

    Assuming that x,y,z>0, b

  7. (2a1b23ac2)3 for a,b,c0

  8. (uv)n(vu)3n+4:(vu)2n+1 for u,v0

  9. x5+1xm+22x22xm+2xxm2 for x0

  10. (z3z+5)2p+1(5+zz3)p+1:(z3z+5)4p for z∉{5;3}

  11. (1+2t)2[1t(t21)1]2 for t∉{2;0;2}

  12. Re-formulate the expression to a single fraction that does not contain any negative exponents.

    4a1z2(x2y)3:(2a)3(xy2z)2


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