Choose the correct simplification of the expression the quantity a to the 2nd power over b to the 3rd power all raised to the 4th power.
A. a to the 6th power over b to the 7th power
B. b^12
C. a^8b^15
D. the quantity a to the 8th power over b to the 12th power
pls help me
(a²/b³)⁴ = a⁸/b¹²
Therefore, D
To simplify the given expression, "the quantity a to the 2nd power over b to the 3rd power all raised to the 4th power," we can use the exponent rule: when a power is raised to another power, we multiply the exponents.
So, let's break it down step by step:
Step 1: Start with the expression (a^2 / b^3)^4.
Step 2: Apply the exponent rule by multiplying the exponents inside the parenthesis:
(a^(2 * 4) / b^(3 * 4)).
Simplifying further:
(a^8 / b^12).
Therefore, the correct simplification of the given expression is: the quantity a to the 8th power over b to the 12th power. So, the correct answer is option D.
To simplify the expression the quantity a^2 / b^3 raised to the 4th power, we need to raise both the numerator and denominator to the 4th power.
This results in (a^2)^4 / (b^3)^4, which can be further simplified to a^8 / b^12.
Therefore, the correct simplification is D. the quantity a to the 8th power over b to the 12th power.