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Simplify. Express your answer using a single exponent.\newline(5n3)3(5n^3)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(5n3)3(5n^3)^3
  1. Apply Power Rule: Apply the power of a power rule to the expression (5n3)3(5n^3)^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 outside the parentheses and an exponent of 33 on nn inside the parentheses. (5n3)3=53×(n3)3(5n^3)^3 = 5^3 \times (n^3)^3
  2. Calculate 535^3: Calculate 535^3.535^3 is 55 multiplied by itself three times.53=5×5×5=1255^3 = 5 \times 5 \times 5 = 125
  3. Calculate (n3)3(n^3)^3: Calculate (n3)3(n^3)^3. Using the power of a power rule, we multiply the exponents. (n3)3=n(3×3)=n9(n^3)^3 = n^{(3 \times 3)} = n^9
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have 53=1255^3 = 125 and (n3)3=n9(n^3)^3 = n^9, so we combine these to get the final simplified expression.\newline(5n3)3=125n9(5n^3)^3 = 125n^9

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