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Simplify. Express your answer using a single exponent.\newline(6z4)2(6z^4)^2

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Q. Simplify. Express your answer using a single exponent.\newline(6z4)2(6z^4)^2
  1. Apply Power Rule: Apply the power of a power rule.\newlineThe power of a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we have (6z4)2(6z^4)^2, which means we need to apply the exponent of 22 to both 66 and z4z^4.\newline(6z4)2=62×(z4)2(6z^4)^2 = 6^2 \times (z^4)^2
  2. Calculate 626^2: Calculate 626^2.\newline626^2 means 66 multiplied by itself, which is 3636.\newline62=366^2 = 36
  3. Calculate (z4)2(z^4)^2: Calculate (z4)2(z^4)^2. Using the power of a power rule, we multiply the exponents 44 and 22. (z4)2=z(42)=z8(z^4)^2 = z^{(4*2)} = z^8
  4. Combine Results: Combine the results.\newlineNow we combine the results from Step 22 and Step 33 to get the final simplified expression.\newline(6z4)2=62×(z4)2=36z8(6z^4)^2 = 6^2 \times (z^4)^2 = 36z^8