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Simplify. Express your answer using a single exponent.\newline(4z3)3(4z^3)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4z3)3(4z^3)^3
  1. Apply Power Rule: Apply the power to a power rule.\newlineWhen raising a power to another power, we multiply the exponents. For the given expression (4z3)3(4z^3)^3, we apply this rule to the variable zz.\newline(4z3)3=43×(z3)3(4z^3)^3 = 4^3 \times (z^3)^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. Simplify (z3)3(z^3)^3: Simplify (z3)3(z^3)^3. We multiply the exponents for zz, which means 33 times 33. (z3)3=z(3×3)=z9(z^3)^3 = z^{(3 \times 3)} = z^9
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have found that 43=644^3 = 64 and (z3)3=z9(z^3)^3 = z^9. Now we combine these results to express the simplified form of the original expression.\newline(4z3)3=64×z9(4z^3)^3 = 64 \times z^9

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