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Simplify. Express your answer using a single exponent.\newline(2c5)4(2c^5)^4

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(2c5)4(2c^5)^4
  1. Apply Power Rule: Apply the power to a power rule.\newlineWhen raising a power to another power, we multiply the exponents. For the expression (2c5)4(2c^5)^4, we apply this rule to the cc term.\newline(2c5)4=24×(c5)4(2c^5)^4 = 2^4 \times (c^5)^4
  2. Simplify 242^4: Simplify 242^4.\newlineCalculate the value of 22 raised to the 44th power.\newline24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16
  3. Simplify (c5)4(c^5)^4: Simplify (c5)4(c^5)^4.\newlineMultiply the exponents for the cc term.\newline(c5)4=c(5×4)=c20(c^5)^4 = c^{(5 \times 4)} = c^{20}
  4. Combine Simplified Terms: Combine the simplified terms.\newlineNow that we have simplified both terms, we can combine them to get the final answer.\newline(2c5)4=16×c20(2c^5)^4 = 16 \times c^{20}

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