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(4×10^(-5))^(-6)

1414) (4×10−5)−6 \left(4 \times 10^{-5}\right)^{-6}

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Full solution

Q. 1414) (4×10−5)−6 \left(4 \times 10^{-5}\right)^{-6}
  1. Apply Power Rule: First, let's apply the power of a power rule which states that (ab)c=a(b∗c) (a^b)^c = a^{(b*c)} . (4×10−5)−6=4−6×(10−5)−6 (4\times10^{-5})^{-6} = 4^{-6} \times (10^{-5})^{-6} .
  2. Calculate 4−64^{-6}: Now, let's calculate 4−64^{-6}. \newline4−6=146=1(22)6=12124^{-6} = \frac{1}{4^6} = \frac{1}{(2^2)^6} = \frac{1}{2^{12}}
  3. Calculate (10−5)−6(10^{-5})^{-6}: Next, calculate (10−5)−6(10^{-5})^{-6}.(10−5)−6=10(−5)∗(−6)=1030(10^{-5})^{-6} = 10^{(-5)*(-6)} = 10^{30}
  4. Multiply Results: Now, multiply the two results together.\newline(1212)×1030(\frac{1}{2^{12}}) \times 10^{30}
  5. Simplify Multiplication: Simplify the multiplication by handling the powers of 1010. 1×1030/2121 \times 10^{30} / 2^{12}
  6. Calculate 2122^{12}: Calculate 2122^{12} to simplify the fraction.\newline212=40962^{12} = 4096
  7. Divide 103010^{30}: Now, divide 103010^{30} by 40964096.\newline10304096\frac{10^{30}}{4096}\newlineOops, this is where I made a mistake. I should have kept the powers of 1010 separate from the fraction involving 2122^{12}.

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