Evaluate. (125^(-(11)/(12)))/(125^(-(1)/(4)))=

Question

Evaluate.  (125^(-(11)/(12)))/(125^(-(1)/(4)))=

Bytelearn · Accepted Answer

Simplify expression using exponents: Simplify the expression using the properties of exponents. We have the expression (125^(-(11)/(12)))/(125^(-(1)/(4))). To simplify, we can use the property of exponents that states a^(m)/a^(n) = a^(m-n) where a is the base and m, n are exponents.Combine exponents using property: Apply the property of exponents to combine the exponents. We subtract the exponent in the denominator from the exponent in the numerator: -(11/12) - (-(1/4)) = -(11/12) + (1/4).Find common denominator for fractions: Find a common denominator to add the fractions. The common denominator for 12 and 4 is 12. So we convert 1/4 to 3/12 and then add it to -11/12. -(11/12) + (3/12) = -11/12 + 3/12 = -8/12.Simplify fraction -8/12: Simplify the fraction -8/12. We can simplify -8/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 4. -8/12 ÷ 4/4 = -2/3.Write expression with new exponent: Write the simplified expression with the new exponent. Now we have 125^(-2/3).Evaluate 125^(-2/3): Evaluate 125^(-2/3). Since 125 is 5^3, we can rewrite 125^(-2/3) as (5^3)^(-2/3). Using the property of exponents (a^(m))^n = a^(m*n), we get 5^(3*(-2/3)) = 5^(-2).Evaluate 5^(-2): Evaluate 5^(-2). The negative exponent means we take the reciprocal of the base raised to the positive exponent. So, 5^(-2) = 1/(5^2).Calculate 5^2: Calculate 5^2. 5^2 is 5 multiplied by itself, which equals 25.Write final answer: Write the final answer. Therefore, 1/(5^2) is 1/25.

Evaluate. $\newline$ $\frac{125^{-\frac{11}{12}}}{125^{-\frac{1}{4}}}=$

Full solution

More problems from Powers with negative bases

Related topics

Evaluate.\newline125−1112125−14= \frac{125^{-\frac{11}{12}}}{125^{-\frac{1}{4}}}= 125−41​125−1211​​=

Evaluate. $\newline$ $\frac{125^{-\frac{11}{12}}}{125^{-\frac{1}{4}}}=$