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Which expression is equivalent to (106)4(10^6)^4?\newlineChoices:\newline(A) 11024\frac{1}{10^{24}}\newline(B) 102410^{24}\newline(C) 11010\frac{1}{10^{10}}\newline(D) 101010^{10}

Full solution

Q. Which expression is equivalent to (106)4(10^6)^4?\newlineChoices:\newline(A) 11024\frac{1}{10^{24}}\newline(B) 102410^{24}\newline(C) 11010\frac{1}{10^{10}}\newline(D) 101010^{10}
  1. Understand the problem: Understand the problem.\newlineWe need to find the equivalent expression for the power of a power, (106)4(10^6)^4.\newlineWhen we raise a power to a power, we multiply the exponents.\newlinea(mn)=a(mn)a^{(m^n)} = a^{(m*n)}
  2. Apply power rule: Apply the power of a power rule.\newline(106)4=106×4(10^6)^4 = 10^{6\times4}\newlineCalculate the product of the exponents.\newline106×4=102410^{6\times4} = 10^{24}
  3. Match with choices: Match the result with the given choices.\newlineThe calculation from Step 22 gives us 102410^{24}, which corresponds to choice (B).