(9^3/6^3)^-1/3
First, we simplify the exponent inside the parentheses:
9^3 = 729
6^3 = 216
So, (9^3/6^3) = 729/216
Next, we simplify the exponent outside the parentheses:
(-1/3) means the cube root of the inverse or reciprocal.
Reciprocal of 729/216 is 216/729.
Cube root of 216/729 is 6/9.
Simplifying further, 6/9 reduces to 2/3.
Therefore, (9^3/6^3)^-1/3 = (729/216)^-1/3 = (216/729)^(1/3) = (2/3) = 0.6667 (rounded to four decimal places).
(8^4/10^4)^-1/4
First, we simplify the exponent inside the parentheses:
8^4 = 4096
10^4 = 10000
So, (8^4/10^4) = 4096/10000
Next, we simplify the exponent outside the parentheses:
(-1/4) means the fourth root of the inverse or reciprocal.
Reciprocal of 4096/10000 is 10000/4096.
Fourth root of 10000/4096 is approximately 1.1225 (rounded to four decimal places).
Therefore, (8^4/10^4)^-1/4 = (4096/10000)^-1/4 = (10000/4096)^(1/4) = 1.1225 (approximately).
or 10/8 = 1.25 (not 1.1225)
because
(8^4/10^4)^-1/4 = (10^4 /8^4)^1/4 = 10/8
You are correct. I apologize for my error in the previous response.
We can simplify the expression as follows:
(8^4/10^4)^-1/4 = (10^4/8^4)^1/4
10/8 is equal to 1.25, so
(10^4/8^4)^1/4 = (1.25)^1/4 = 1.0569 (rounded to four decimal places).
Therefore, (8^4/10^4)^-1/4 = (10^4/8^4)^1/4 = 1.0569 (approximately).
NO !!!!
(10^4/8^4)^1/4 = (1.25)^1/4 = 1.0569
NO !!!!
(10^4/8^4)^1/4 = 10/4
not (10/8)^1/4
(1.25^4)^1/4 = 1.25
I apologize for my mistake again. You are correct. Here is the correct solution:
We can simplify the expression as follows:
(8^4/10^4)^-1/4 = (10^4/8^4)^1/4
10/8 is equal to 1.25, so
(10^4/8^4)^1/4 = (1.25)^4/4 = 1.25
Therefore, (8^4/10^4)^-1/4 = (10^4/8^4)^1/4 = 1.25.
Whew !!!!!
I apologize again for the confusion caused by my earlier mistake. Thank you for bringing it to my attention and allowing me to correct it.
To simplify the expression (9^3/6^3)^-1/3, we need to follow the order of operations or the PEMDAS rule, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's break down the expression step by step:
Step 1: Simplify the numerator and denominator inside the parentheses.
9^3 = 729
6^3 = 216
So, the expression becomes (729/216)^-1/3.
Step 2: Simplify the fraction inside the parentheses.
Since there are no common factors between 729 and 216, we cannot simplify the fraction further.
The expression becomes (729/216)^-1/3.
Step 3: Apply the negative exponent.
To apply the negative exponent, we need to flip the fraction.
The expression becomes (216/729)^1/3.
Step 4: Evaluate the exponent.
(216/729)^1/3 = (0.2963)^1/3 = 0.672
So, the value of the expression (9^3/6^3)^-1/3 is approximately 0.672.