Question

A) work out the value of 81^-1/4 b) 64 × 4^5x can be written in the form 2^k where k is an expression in terms of x. find k

Answer 1

The value of 81^-1/4 is 1/3, and 64 × 4^5x can be written as 2^k where k = 6 + 10x.

Step-by-step explanation:

To answer your questions:

A) Calculate the value of 81-1/4

To calculate the value of 81-1/4, realize that 81 is 3 raised to the 4th power (34). So, 81-1/4 is the same as (34)-1/4. The negative exponent indicates the reciprocal, and the fractional exponent indicates a root. Therefore, 81-1/4 is equivalent to 1/3, since it's the fourth root of 81 taken to the power of -1.

B) Express 64 × 45x as 2k

Write 64 × 45x in the form of 2k. Since 64 is 26 and 4 is 22, your expression becomes 26 × (22)5x. Apply the power of a power rule and you get 26 × 210x or 26+10x. Therefore, k equals 6+10x.