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Simplify. Express your answer using a single exponent.\newline(10x3)2(10x^3)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(10x3)2(10x^3)^2
  1. Apply Power Rule: Apply the power of a power rule to (10x3)2(10x^3)^2. The power of a power rule states that (an)m=an∗m(a^n)^m = a^{n*m}. We will apply this rule to both the numerical part (102)(10^2) and the variable part (x3∗2)(x^{3*2}). (10x3)2=(102)∗(x3∗2)(10x^3)^2 = (10^2) * (x^{3*2})
  2. Calculate 10210^2: Calculate the numerical part 10210^2.\newline102=10×10=10010^2 = 10 \times 10 = 100
  3. Calculate x3×2x^{3\times2}: Calculate the variable part x3×2x^{3\times2}.\newlinex3×2=x6x^{3\times2} = x^{6}
  4. Combine Numerical and Variable Parts: Combine the numerical and variable parts to express the final answer.\newline(10x3)2=100×x6(10x^3)^2 = 100 \times x^6

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