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Simplify. Express your answer using a single exponent.\newline(4b9)4(4b^{9})^{4}

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4b9)4(4b^{9})^{4}
  1. Apply Power Rule: Apply the power of a power rule to the expression (4b9)4(4b^9)^4. 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 coefficient and the variable with its exponent. (4b9)4=44×(b9)4(4b^9)^4 = 4^4 \times (b^9)^4
  2. Calculate 444^4: Calculate the value of 444^4. \newline44=4×4×4×4=2564^4 = 4 \times 4 \times 4 \times 4 = 256
  3. Apply Power Rule to b9b^9: Apply the power of a power rule to (b9)4(b^9)^4.\newline(b9)4=b(9∗4)=b36(b^9)^4 = b^{(9*4)} = b^{36}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineThe simplified expression is 256×b36.256 \times b^{36}.

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