%5E3%2F4a%5E3b%5E7.jpeg "(2a^2b^3)^3/4a^3b^7")
Simplifying the Expression: (2a^2b^3)^3/4a^3b^7
Introduction
In this article, we will simplify the algebraic expression (2a^2b^3)^3/4a^3b^7. To simplify this expression, we will use the rules of exponents and algebraic manipulations.
Step 1: Evaluate the Exponent
First, let's evaluate the exponent of ^3 outside the parentheses. Using the rule of exponents that states a^(mn) = (a^m)^n, we can rewrite the expression as:
(2^3)(a^6)(b^9) / 4a^3b^7
Step 2: Simplify the Numerator
Next, let's simplify the numerator. Using the rule of exponents that states a^m * a^n = a^(m+n), we can rewrite the expression as:
8a^6b^9 / 4a^3b^7
Step 3: Simplify the Denominator
Now, let's simplify the denominator. We can rewrite the expression as:
8a^6b^9 / (2^2)(a^3)(b^7)
Step 4: Cancel Out Common Factors
Next, let's cancel out common factors between the numerator and denominator. We can cancel out a^3 and b^7 from both numerator and denominator:
8a^3b^2 / 4
Step 5: Simplify the Final Expression
Finally, we can simplify the final expression by canceling out common factors:
2a^3b^2
Therefore, the simplified expression is 2a^3b^2.
