Simplify (2b^4)^-1

Problem

(2*b^4)^(−1)

Solution

1. Apply the power of a product rule, which states that (x*y)^n=x^n*y^n

(2*b^4)^(−1)=2^(−1)*(b^4)^(−1)

2. Apply the power of a power rule to the variable term, which states that (x^a)^b=x^(a*b)

2^(−1)*(b^4)^(−1)=2^(−1)*b^(−4)

3. Apply the negative exponent rule, which states that x^(−n)=1/(x^n) to move the terms to the denominator.

2^(−1)*b^(−4)=1/(2^1*b^4)

4. Simplify the expression by removing the exponent of 1.

1/(2^1*b^4)=1/(2*b^4)

Final Answer

(2*b^4)^(−1)=1/(2*b^4)

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