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Simplify. Express your answer using a single exponent.\newline(5z8)2(5z^8)^2\newline_____________

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Q. Simplify. Express your answer using a single exponent.\newline(5z8)2(5z^8)^2\newline_____________
  1. Apply power of product rule: Apply the power of a product rule.\newlineThe power of a product rule states that when an entire product is raised to a power, you can apply the exponent to each factor in the product separately.\newline(5z8)2=(5)2×(z8)2(5z^8)^2 = (5)^2 \times (z^8)^2
  2. Simplify (5)2(5)^2: Simplify (5)^2\.\newlineCalculate the square of 55\.\newline(5)2=5×5=25(5)^2 = 5 \times 5 = 25
  3. Apply power of power rule: Simplify (z8)2(z^8)^2 using 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.\newline(z8)2=z(8×2)=z16(z^8)^2 = z^{(8 \times 2)} = z^{16}
  4. Combine simplified terms: Combine the simplified terms.\newlineNow that we have simplified both terms, we can combine them to express the final answer.\newline(5z8)2=25×z16=25z16(5z^8)^2 = 25 \times z^{16} = 25z^{16}

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