%5E3.jpeg "(3/2b^4)^3")
(3/2b^4)^3: Understanding Exponents and Order of Operations
In mathematics, understanding exponents and order of operations is crucial to simplify complex expressions. One such expression is (3/2b^4)^3. In this article, we will break down this expression and evaluate it step by step.
What does the expression mean?
The expression (3/2b^4)^3 can be read as "3 divided by 2, multiplied by b to the power of 4, raised to the power of 3". It's a combination of division, multiplication, exponentiation, and another exponentiation.
Step 1: Evaluate the Expression inside the Parentheses
First, let's evaluate the expression inside the parentheses: 3/2b^4. To do this, we need to follow the order of operations (PEMDAS):
- Divide 3 by 2:
3/2 = 1.5 - Raise b to the power of 4:
b^4 - Multiply 1.5 by b^4:
1.5b^4
So, the expression inside the parentheses is equivalent to 1.5b^4.
Step 2: Raise the Expression to the Power of 3
Now, we need to raise the entire expression to the power of 3:
(1.5b^4)^3
To do this, we can use the power rule of exponents, which states that (a^m)^n = a^(mn). In this case, a = 1.5b^4, m = 4, and n = 3.
Applying the power rule, we get:
(1.5b^4)^3 = 1.5^(3)b^(4*3) = 1.5^3*b^(12)
Simplifying the Expression
Finally, we can simplify the expression by evaluating the exponent of 1.5:
1.5^3 = 3.375
So, the final simplified expression is:
3.375b^(12)
Conclusion
In this article, we have successfully evaluated the expression (3/2b^4)^3 by following the order of operations and applying the power rule of exponents. The final result is 3.375b^(12). Remember to always follow the rules of exponents and order of operations to simplify complex expressions.
