simplify (6x^-2)^2(0.5x)^4
I think I know the answer is 2.25 but my work is wrong my teacher said and I need to get this right so plz any help is fine
(6x^-2)^2 = 36 x^-4
(1/2 x)^4 = 1/16 x^4
multiply and you get 36/36 = 9/4 = 2.25
If you want us to analyze your work, you need to show it!
To simplify the given expression (6x^-2)^2(0.5x)^4, let's break it down step by step:
First, we'll focus on simplifying each individual factor within the parentheses using the power rule.
Starting with (6x^-2)^2:
Step 1: Square the base, which is 6: (6)^2 = 36.
Step 2: For the exponent, multiply it by 2: -2 * 2 = -4.
Step 3: Rewrite the expression with the simplified values: 36x^-4.
Next, let's simplify (0.5x)^4:
Step 1: Square the base, which is 0.5: (0.5)^2 = 0.25.
Step 2: For the exponent, multiply it by 4: 1 * 4 = 4.
Step 3: Rewrite the expression with the simplified values: 0.25x^4.
Now that we have simplified both factors separately, we can multiply them together:
(36x^-4) * (0.25x^4)
When multiplying variables with the same base, add the exponents:
36 * 0.25 = 9
For the 'x' term, add the exponents: -4 + 4 = 0.
Thus, the simplified expression is:
9x^0
Any term with an exponent of zero is equal to 1, so x^0 reduces to 1:
9 * 1 = 9
Therefore, the simplified expression is 9.