Final answer:
The correct value of 'x' is found by applying exponent rules to the expression b(b⁴ * b³)². After simplifying, we get b¹¹ = b³x, where 3x = 9 and x = 3, which makes option (c) x = 9 the correct answer.
Step-by-step explanation:
The student has asked about simplifying an expression with exponents and determining the value of 'x' in the equivalent expression b(b⁴ * b³)² = b³x. To solve this problem, we need to apply the rules of exponents.
Firstly, we can simplify the expression inside the parentheses by adding the exponents of the same base 'b'. This gives us:
b⁴ * b³ = b⁴+3 = b⁷
Next, when we raise the expression to the square (the exponent of 2 outside the parentheses), we multiply the exponents:
(b⁷)² = b⁷*2 = b⁹²
Now, we have the simplified expression:
b * b¹⁴
Multiplying the bases with the same exponent involves adding the exponents:
b¹ * b¹⁴ = b¹+9² = b¹¹
Finally, we compare the original expression to the given expression (b³x):
b¹¹ = b³x
Since the bases are the same, their exponents must be equal, meaning:
3x = 9
Therefore, to find 'x', we divide both sides of the equation by 3:
x = 9/3 = 3
So the value of 'x' is 3. This means that option (b) x = 6 is an error. Answer (c) x = 9 is the correct choice.