Simplify
(16x^8)^-3/4
1) 16^-3/4*(x^8)^-3/4
2) -12*x^-6
3) -12*1/x^6
4) -12/x^6
Which step is incorrect? Please help!!
16^-3/4 = 1/16^3/4 = 1/2^3 = 1/8
1/x^(24/4) = 1/x^6 = x^-6
so I get
(1/8)x^-6
To simplify the expression (16x^8)^-3/4, you need to follow the rules of exponentiation.
Step 1: Apply the power to each factor individually.
(16x^8)^-3/4 can be written as (16)^(-3/4)*(x^8)^(-3/4).
Step 2: Simplify each factor individually.
For the first factor, (16)^(-3/4), when a number is raised to a negative exponent, you can rewrite it as the reciprocal of the number raised to the positive exponent. Therefore, (16)^(-3/4) can be simplified as 1/(16)^(3/4).
For the second factor, (x^8)^(-3/4), the rule for raising a power to another power states that you multiply the exponents. Applying this rule gives us x^(8*(-3/4)).
Step 3: Simplify further if possible.
For the first factor, 1/(16)^(3/4), you can evaluate (16)^(3/4) to get the fourth root of 16, which is 2. Therefore, this factor simplifies to 1/2^3.
For the second factor, x^(8*(-3/4)) can be simplified as x^(-6).
Step 4: Combine the simplified factors.
Putting it all together, we have (16x^8)^-3/4 = (1/2^3)*(x^(-6)).
Simplifying the first factor gives us 1/(2^3) = 1/8.
Therefore, the final simplification is (16x^8)^-3/4 = (1/8)*(x^-6).
Comparing the provided options:
1) 16^-3/4*(x^8)^-3/4 - This option is correct and represents the simplified form mentioned above.
2) -12*x^-6 - This does not match the correct simplified form as it omits the fractional term.
3) -12*1/x^6 - This option is incorrect as it does not consider the fractional term.
4) -12/x^6 - This option is incorrect as it does not include the correct simplified form (1/8).
Therefore, the incorrect step is represented in option 2.