How do you simplify 16⁻³/₄?

To simplify the expression \( 16^{-3/4} \), follow these steps:

Step 1: Rewrite the Base

First, recognize that \( 16 \) can be expressed as a power of \( 2 \):

• Since \( 16 = 2^4 \), we can rewrite the expression:

So, \( 16^{-3/4} = (2^4)^{-3/4} \).

Step 2: Apply the Power of a Power Rule

Next, use the rule of exponents that states \( (a^m)^n = a^{m \cdot n} \):

• Multiply the exponents:

This gives us \( 2^{4 \cdot (-3/4)} = 2^{-3} \).

Step 3: Simplify the Exponent

Now, simplify \( 2^{-3} \):

• Recall that a negative exponent indicates a reciprocal:

Thus, \( 2^{-3} = \frac{1}{2^3} \).

Step 4: Calculate the Final Value

Finally, calculate \( 2^3 \):

• Since \( 2^3 = 8 \), we find:

Therefore, \( 16^{-3/4} = \frac{1}{8} \).

Final Result

The simplified form of \( 16^{-3/4} \) is \( \frac{1}{8} \).