having a little trouble following the steps to complete this problem.
Rewrite each expression with a positive ration exponent. Simplify if possible:
16^-3/4
16^-3/4
= 1/16^(3/4)
= 1/(16^(1/4))^3
= 1/2^3
= 1/8
thanks!
To rewrite the expression 16^(-3/4) with a positive rational exponent, you can use the following steps:
Step 1: Understand the exponent rules.
In this case, the negative exponent indicates that you need to take the reciprocal of the base raised to the positive exponent.
Step 2: Rewrite the expression with a positive exponent by taking the reciprocal.
Since 16^(-3/4) has a negative exponent, you can rewrite it as 1/16^(3/4).
Step 3: Simplify the expression if possible.
To simplify further, you need to evaluate 16^(3/4), which means taking the fourth root of 16 and then raising it to the power of 3.
Step 4: Calculate the fourth root of 16.
The fourth root of 16 can be found by raising 16 to the power of 1/4. Since 16^(1/4) equals 2, the fourth root of 16 is 2.
Step 5: Raise the fourth root of 16 to the power of 3.
The next step is to raise 2 to the power of 3. This gives you 2^3, which is equal to 8.
Therefore, the expression 16^(-3/4) can be rewritten as 1/8.