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Simplify. Express your answer using a single exponent.\newline(4z4)3(4z^4)^3

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Q. Simplify. Express your answer using a single exponent.\newline(4z4)3(4z^4)^3
  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. For the expression (4z4)3(4z^4)^3, we apply this rule to both the numerical coefficient and the variable with its exponent.\newline(4z4)3=43×(z4)3(4z^4)^3 = 4^3 \times (z^4)^3
  2. Calculate 434^3: Calculate 434^3.\newlineTo simplify 434^3, we multiply 44 by itself three times.\newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  3. Multiply z exponents: Multiply the exponents for z.\newlineWe multiply the exponents of z according to the power of a power rule.\newline(z4)3=z(4×3)=z12(z^4)^3 = z^{(4 \times 3)} = z^{12}
  4. Combine results: Combine the results.\newlineWe combine the results from Step 22 and Step 33 to get the final simplified expression.\newline(4z4)3=43×(z4)3=64×z12=64z12(4z^4)^3 = 4^3 \times (z^4)^3 = 64 \times z^{12} = 64z^{12}