Simplify ((16x^-10)/(x^6))^(-1/4)

Problem

((16*x(−10))/(x6))(−1/4)

Solution

1. Simplify the expression inside the parentheses by using the quotient rule for exponents, am/an=a(m−n)

(16*x(−10))/(x6)=16*x(−10−6)

16*x(−10−6)=16*x(−16)

2. Apply the power of a product rule (a*b)n=an*bn to the simplified expression.

(16*x(−16))(−1/4)=16(−1/4)⋅(x(−16))(−1/4)

3. Evaluate the numerical part by rewriting 16 as a power of 2 and applying the power of a power rule (am)n=a(m*n)

16(−1/4)=(2)(−1/4)

(2)(−1/4)=2(−1)

2(−1)=1/2

4. Evaluate the variable part by multiplying the exponents.

(x(−16))(−1/4)=x(−16⋅−1/4)

x(−16⋅−1/4)=x4

5. Combine the results to find the final simplified form.

1/2⋅x4=(x4)/2

Final Answer

((16*x(−10))/(x6))(−1/4)=(x4)/2

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