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Rewrite the expression in the form b^(n). b^(4)*b^(-(1)/(4))=

Rewrite the expression in the form bn b^{n} .\newlineb4⋅b−14= b^{4} \cdot b^{-\frac{1}{4}}=

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Q. Rewrite the expression in the form bn b^{n} .\newlineb4⋅b−14= b^{4} \cdot b^{-\frac{1}{4}}=
  1. Using exponent property: To simplify the expression b4⋅b−14b^{4}\cdot b^{-\frac{1}{4}}, we use the property of exponents that states when we multiply two powers with the same base, we add their exponents.\newlineSo, b4⋅b−14=b4+(−14)b^{4}\cdot b^{-\frac{1}{4}} = b^{4 + \left(-\frac{1}{4}\right)}.
  2. Performing addition of exponents: Now we perform the addition of the exponents: 4+(−(1)/(4))=4−1/4=16/4−1/4=15/44 + (-(1)/(4)) = 4 - 1/4 = 16/4 - 1/4 = 15/4. So, b4∗b−(1)/(4)=b15/4b^{4}*b^{-(1)/(4)} = b^{15/4}.

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