Evaluate 12-4^(3/8)

Problem

12−4(3/8)

Solution

1. Rewrite the base of the exponential term as a power of 2 to simplify the expression.

4=2

2. Substitute the new base into the expression and apply the power of a power rule, which states (am)n=a(m⋅n)

4(3/8)=(2)(3/8)

3. Multiply the exponents to simplify the term.

2⋅3/8=6/8

4. Reduce the fraction in the exponent to its simplest form.

6/8=3/4

5. Express the result in radical form if necessary, noting that a(m/n)=√(n,am)

2(3/4)=√(4,2)

6. Calculate the value inside the radical.

2=8

7. Combine the terms back into the original expression.

12−√(4,8)

Final Answer

12−4(3/8)=12−√(4,8)

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