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Simplify. Express your answer as the given base raised to a single exponent.\newline(47)4(4^7)^4

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Power of a power: integer basesright chevron icon

Full solution

Q. Simplify. Express your answer as the given base raised to a single exponent.\newline(47)4(4^7)^4
  1. Recognize expression structure: Step 11: Recognize the expression structure.\newlineWe have 47)4 whichmeans$44^7)^4\, which means \$4 raised to the 77th power, and then that result raised to the 44th power.
  2. Apply power property: Step 22: Apply the power of a power property.\newlineUsing the rule (am)n=am∗n(a^m)^n = a^{m*n}, we calculate:\newline(47)4=47∗4(4^7)^4 = 4^{7*4}
  3. Perform multiplication: Step 33: Perform the multiplication.\newline7×4=287 \times 4 = 28\newlineSo, (47)4=428(4^7)^4 = 4^{28}

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