I realized that I was typing the problems incorrectly. So here is the correct problem,
27^-2/3
____________
27 ^-1/3
Thank you Maxine, I will get started on helping you with this right away.
You're welcome
27^-2/3
____________
27 ^-1/3
First with your given problem, you need to convert each negative exponent into a fraction. We will start with the denominator.
27 ^ -1/3 turns into: 1/(cube root of 27)
1/(cube root of 27) = 3
Your problem now currently looks like this:
27^-2/3
____________
1/3
Now let's do the same for the numerator.
27 ^ -2/3 turns into: 1 / 27 ^ (2/3)
27 ^ (2/3) = 3^2 = 9
Your problem now currently looks like this:
1/9
____________
1/3
We now have to divide the fractions, so we use the reciprocal of the denominator and then multiply.
Your problem is now
(1/9) x (3/1)
1/9 of 3 is 1/3.
Your final answer is 1/3.
To solve this problem, we need to understand two concepts: negative exponents and fractional exponents.
First, let's start with negative exponents. When a number has a negative exponent, it means that the number should be moved to the opposite side of the fraction and the exponent becomes positive. For example, if we have 2^-3, it is equivalent to 1/2^3.
Next, let's understand fractional exponents. A fractional exponent represents taking the root of a number. For example, x^(1/2) represents the square root of x, and x^(1/3) represents the cube root of x.
Using these concepts, let's simplify the expression step by step:
Step 1: Apply negative exponents to move the numbers with negative exponents to the opposite side of the fraction:
(27^(-2/3)) / (27^(-1/3))
Step 2: Simplify the exponents:
(1/27^(2/3)) / (1/27^(1/3))
Step 3: Combine the fractions by multiplying the numerator and denominator by the reciprocal of the fraction in the denominator:
(1/27^(2/3)) * (27^(1/3)/1)
Step 4: Apply the rule of exponents for multiplication and division: When you have the same base with different exponents, you can add or subtract the exponents.
(1/27^(2/3 + 1/3))
Step 5: Simplify the exponents by adding:
(1/27^(3/3))
Step 6: 3/3 is equal to 1, so the expression becomes:
1/27^1
Step 7: The expression 27^1 is equal to 27, so the final simplified expression is:
1/27
Therefore, the value of the original expression 27^(-2/3) / 27^(-1/3) is 1/27.