%5E3.jpeg "(12a^3b^5/4a^6b^3)^3")
Simplifying Exponents: A Step-by-Step Guide
In this article, we will tackle the simplification of the expression (12a^3b^5/4a^6b^3)^3. This expression may seem daunting at first, but with a solid understanding of exponent rules, we can break it down and simplify it step by step.
Step 1: Understand the Expression
The given expression is (12a^3b^5/4a^6b^3)^3. Our goal is to simplify this expression by applying the rules of exponents.
Step 2: Apply the Power Rule
The power rule of exponents states that (a^m)^n = a^(mn). In our expression, we have (12a^3b^5/4a^6b^3)^3. We can apply the power rule to each term separately.
Numerator:
(12^3) = 12^3(since 12 is a constant)(a^3)^3 = a^(3*3) = a^9(b^5)^3 = b^(5*3) = b^15
Denominator:
(4^3) = 4^3(since 4 is a constant)(a^6)^3 = a^(6*3) = a^18(b^3)^3 = b^(3*3) = b^9
Step 3: Simplify the Expression
Now, let's simplify the expression by combining the numerator and denominator:
((12^3)*(a^9)*(b^15))/((4^3)*(a^18)*(b^9))
Step 4: Simplify Further
Simplify the constants:
(12^3) = 1728(4^3) = 64
Now, rewrite the expression:
(1728*a^9*b^15)/(64*a^18*b^9)
Final Simplification
Since we have a common base a in the numerator and denominator, we can simplify the exponent of a:
(1728*b^15)/(64*b^9)
=(27*b^6)
And that's the final answer! The simplified expression is (27*b^6).
