Compute:
18×30×53×221^8 \times 3^0 \times 5^3 \times 2^218×30×53×22
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18×30×53×22=(1×1×1×1×1×1×1×1)×1×(5×5×5)×(2×2)=1×1×125×4=5001^8 \times 3^0 \times 5^3 \times 2^2\\[1em] = (1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1) \times 1 \times (5 \times 5 \times 5) \times (2 \times 2)\\[1em] = 1 \times 1 \times 125 \times 4 \\[1em] = 50018×30×53×22=(1×1×1×1×1×1×1×1)×1×(5×5×5)×(2×2)=1×1×125×4=500
Hence, 18×30×53×22=5001^8 \times 3^0 \times 5^3 \times 2^2 = 50018×30×53×22=500
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If [mn]x−1=[nm]x−5\Big[\dfrac{m}{n}\Big]^{x-1} = \Big[\dfrac{n}{m}\Big]^{x-5}[nm]x−1=[mn]x−5, the value of x is:
3
-3
13\dfrac{1}{3}31
−13-\dfrac{1}{3}−31
[17]−3×7−1×[149]\Big[\dfrac{1}{7}\Big]^{-3} \times 7^{-1} \times \Big[\dfrac{1}{49}\Big][71]−3×7−1×[491] is equal to:
-1
17\dfrac{1}{7}71
-7
1
(47)2×(4−3)4(4^7)^2 \times (4^{-3})^4(47)2×(4−3)4
(2−9÷2−11)3(2^{-9} ÷ 2^{-11})^3(2−9÷2−11)3
