Question

8^(1/6) * 2^x = 32^(1/2)
Work out the exact value of x.
a) 1
b) 2
c) 3
d) 4

Answer 1

The exact value of x in the equation 8^(1/6) * 2^x = 32^(1/2) is found to be 2 after expressing all terms with the base of 2 and simplifying the equation accordingly. Therefore, the exact value of x is 2.

Step-by-step explanation:

To work out the exact value of x in the equation 8^(1/6) * 2^x = 32^(1/2), we first need to express all terms with the same base. Since 8 is 2 cubed (2^3) and 32 is 2 to the fifth power (2^5), the equation can be rewritten using the base of 2.

Here is the step-by-step simplification:

• 8^(1/6) = (2^3)^(1/6) = 2^(3/6) = 2^(1/2)
• 32^(1/2) = (2^5)^(1/2) = 2^(5/2)
• Now we combine these into the original equation: 2^(1/2) * 2^x = 2^(5/2)

Now we can use the rule that when we multiply two exponents with the same base, we add the exponents:

(1/2) + x = (5/2)

Thus, x = (5/2) - (1/2) = 4/2 = 2.

Therefore, the exact value of x is 2.