I am not understanding this problem
3^-1x^4/3^3x^-7
The negative exponents is messing me up. could some one explan a easy why to do it.
I think you mean that you have 3 raised to a -1 power divided by 3^3. What you do with negative powers is just moved them up or down in the fraction to make the power positive.
so, you can move the 3 to the denominator as 3^1 power now combine the 1st power with the 3rd power and you will have 3^4 = 81.
You can move the x^-7 to the top of the fraction to get x^7 and you multiply time x^4/3 which means you add 7 and 4/3 to get the powe for x.
So would my answer be x^11/3^-4
the proble is simplify and write using positive exponents only:
3^-1x^4/
3^3x^-7
Sure! I can help explain how to solve the problem. To simplify the expression with negative exponents, you can follow these steps:
Step 1: Start by handling the negative exponent. Whenever you have a negative exponent, you can rewrite it by moving the term to the opposite side of the fraction and changing the sign of the exponent. So, in our case, we have 3^-1, which can be rewritten as 1/3.
Rewritten expression: (1/3)(x^4)/3^3x^-7
Step 2: Simplify the powers of 3. 3^3 equals 3 x 3 x 3, which is equal to 27.
Rewritten expression: (1/3)(x^4)/27x^-7
Step 3: Combine the x-terms using the rule of exponents. When you divide two variables with the same base but different exponents, you subtract the exponents. In our case, x^4/x^-7 can be simplified as x^(4-(-7)), which is equal to x^11.
Rewritten expression: (1/3)/27x^11
Step 4: Perform the division. To divide by a fraction, we multiply by its reciprocal. So, in this case, we need to multiply by the reciprocal of 27, which is 1/27.
Final simplified expression: (1/3) * (1/27) * x^11
Step 5: Simplify the fractions. Multiply 1/3 by 1/27 to get 1/81.
Final simplified expression: (1/81) * x^11
Therefore, the simplified expression for 3^-1 * x^4 / 3^3 * x^-7 is (1/81) * x^11.