Can you please advise if I did this problem correctly:
(4X5^Y6^z)2^ x (5X9^Y12^Z)3^
(16X7^Y8^Z2^) x (125X12^Y15^z3^)
2000X19^Y23^Z5^
thank you
Let's go through each problem step by step.
1. (4X5^Y6^z)2^ x (5X9^Y12^Z)3^
To solve this problem, we need to simplify each expression and then multiply them together.
Starting with the first expression:
(4X5^Y6^z)2^ = (4X5^(Y6^z))^2 = 4^2 X 5^(2Y6^z) = 16 X 5^(2Y6^z)
Next, simplifying the second expression:
(5X9^Y12^Z)3^ = (5X9^(Y12^Z))^3 = 5^3 X 9^(3Y12^Z) = 125 X 9^(3Y12^Z)
Now, multiplying the two simplified expressions together:
(16 X 5^(2Y6^z)) X (125 X 9^(3Y12^Z)) = 16 X 125 X 5^(2Y6^z) X 9^(3Y12^Z)
So, the final answer is 2000 X 5^(2Y6^z) X 9^(3Y12^Z).
2. (16X7^Y8^Z2^) x (125X12^Y15^z3^)
For this problem, we again need to simplify each expression and then multiply them together.
Starting with the first expression:
(16X7^Y8^Z2^) = 16 X 7^(Y8^Z2^) = 16 X 7^(Y(8^Z2^)) = 16 X 7^(Y(64^Z))
Next, simplifying the second expression:
(125X12^Y15^z3^) = 125 X 12^(Y15^z3^) = 125 X 12^(Y(15^z3^))
Now, multiplying the two simplified expressions together:
(16 X 7^(Y(64^Z))) X (125 X 12^(Y(15^z3^))) = 16 X 125 X 7^(Y(64^Z)) X 12^(Y(15^z3^))
So, the final answer is 2000 X 7^(Y(64^Z)) X 12^(Y(15^z3^)).
3. 2000X19^Y23^Z5^
This expression does not need simplification, as it is already in its simplest form.
So, the final answer is 2000 X 19^Y23^Z5^.
Please note that I have simplified the expressions assuming that the exponents apply to the entire term that follows them. If there are any specific instructions or conventions to apply the exponents differently, please let me know and I will adjust the answer accordingly.
To check if you did each problem correctly, let's break down each expression:
1. (4X5^Y6^z)2^ x (5X9^Y12^Z)3^
To simplify this expression, follow the order of operations (PEMDAS/BODMAS):
First, calculate the exponents within each parenthesis:
- In the first parenthesis: 5^Y6^z
- In the second parenthesis: 9^Y12^Z
Next, simplify the expression by multiplying:
(4 X (5^Y6^z))^2 X (5 X (9^Y12^Z))^3
It seems like you have correctly simplified the expression. However, without knowing the specific values of Y, Z, and the exponents, I cannot provide an exact answer.
2. (16X7^Y8^Z2^) x (125X12^Y15^z3^)
Again, let's simplify this expression step by step:
(16 X (7^Y8^Z2^)) X (125 X (12^Y15^z3^))
Just like the first problem, we cannot evaluate the expression without specific values for Y, Z, and the other exponents. However, the expression seems to be correctly simplified.
3. 2000X19^Y23^Z5^
This expression seems to be fully simplified since there are no additional operations indicated. However, without knowing the specific values of Y, Z, and the exponents, I cannot provide a numerical answer.
To fully determine the accuracy of your work, it would be necessary to know the values of Y, Z, and the exponents involved.