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52(10)−45^2(10)^{-4}

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Full solution

Q. 52(10)−45^2(10)^{-4}
  1. Identify Operation: Identify the operation needed for the exponents.\newlineWe need to simplify the expression 52(10)−45^2(10)^{-4}. This involves dealing with powers and their exponents.
  2. Simplify Using Exponents: Simplify the expression using the properties of exponents.\newlineWe know that 525^2 means 55 multiplied by itself, which is 2525. The expression (10)−4(10)^{-4} means 11 divided by 10410^4. So we can rewrite the expression as 25×110425 \times \frac{1}{10^4}.
  3. Calculate 10410^4: Calculate 10410^4.\newline10410^4 means 1010 multiplied by itself 44 times, which is 10,00010,000.
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have 25×110425 \times \frac{1}{10^4}, which is 2510,000.\frac{25}{10,000}.
  5. Simplify Fraction: Simplify the fraction.\newlineWe can simplify 2510,000\frac{25}{10,000} by dividing both the numerator and the denominator by 2525. This gives us 1400\frac{1}{400}.

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