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Simplify. Express your answer using a single exponent.\newline(4t4)3(4t^4)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4t4)3(4t^4)^3
  1. Apply Power Rule: Apply the power of a power rule to the expression (4t4)3(4t^4)^3. The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have an exponent of 33 being applied to both 44 and t4t^4. (4t4)3=43×(t4)3(4t^4)^3 = 4^3 \times (t^4)^3
  2. Calculate 434^3: Calculate 434^3.\newline434^3 is 44 multiplied by itself 33 times.\newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  3. Calculate (t4)3(t^4)^3: Calculate (t4)3(t^4)^3. Using the power of a power rule, we multiply the exponents 44 and 33. (t4)3=t(4×3)=t12(t^4)^3 = t^{(4 \times 3)} = t^{12}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have found that 43=644^3 = 64 and (t4)3=t12(t^4)^3 = t^{12}. Now we combine these to express the simplified form of the original expression.\newline(4t4)3=64×t12(4t^4)^3 = 64 \times t^{12}

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