Evaluate the expression. a. 3^1 / 4 ·9^-5 / 8 b. 2^3 / 4 ·4^-3 / 2

Name: Problem 6, Chapter 3: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-05-12T19:38:54-08:00
Duration: 2 min 47 s
Channel: Priyanka Sadarangani
Description: Evaluate the expression. a. 3^1 / 4 ·9^-5 / 8 b. 2^3 / 4 ·4^-3 / 2

Evaluate the expression. a. 3^1 / 4 ·9^-5 / 8 b. 2^3 / 4...

Key Concepts

Fractional Exponents

Fractional exponents provide a way to represent radicals and roots. The numerator denotes the power and the denominator represents the root. Understanding fractional exponents is critical for converting between radical notation and exponential form, which is often a key step in simplifying and evaluating expressions.

Properties of Exponents

This concept encompasses the rules used to manipulate expressions with exponents, including the product of powers rule (adding exponents when multiplying like bases), the power of a power rule (multiplying exponents), and the negative exponent rule (expressing negative exponents as reciprocals). It is essential for simplifying complex expressions involving powers.

Common Base Conversion

This concept involves rewriting numbers as powers of a common base, which greatly simplifies the manipulation and comparison of exponential expressions. By expressing different numbers with the same base, one can directly apply the rules of exponents to combine and simplify the expressions.

Transcript

00:01 In this question we have to evaluate the expressions and part a that is three raised to the power one by four dot nine raised to the power minus five by eight okay so these are the exponents okay so we will use the law of exponents i am writing down first the law then we will use in our part a and part b so it is that is law three that b raised to the power x whole race to the power y this can be written as b raised to the power x y okay and now and other one that is b raised to the power x dot b raised to the power y it will be b raised to the power x plus y okay so we will use these laws one and two okay in our question so now moving again to the question it will be three raised to the power one by four dot this nine can be written as three square okay so it will be three square and whole rest to the power minus five by eight and now it will be three raised to the power one by four dot it will be okay b raised to the power x whole rest to the power y so it will be b to the power x y from this rule and it will be three to the power two multiply by minus 5 by 8 it will be minus 5 by 4 okay and now we will use this law that is b raised to the power x multiply by b raised to the power x plus y okay we will add the exponent so it will be 3 to the power 1 by 4 minus 5 by 4 so it will be 3 raised to the power minus 4 by 4 or we can say minus 1 and now 3 rest to the power minus 1 can be written as 1 by 3 so 1 by 3 will be the answer of part a of this question okay and now part b so part b is 2 raised to the power 3 by 4 4 raised to the power negative 3 by 2 again 2 raise to the power 3 by 4 dot 4 can be written as 2 square so it will be 2 square raised to the power negative 3 by 2 okay and now it will be 2 raised to the power 3 by 4 and we will use the this law here that is b raised to the power x whole raise to the power y that will be b raised to the power x y so it will be 2 raised to the power 2 2 multiply by minus 3 by 2 it will be minus 3 okay and now we will use b raised to the power x dot b raised to the power y it will be b raised to the power x plus y so 3 by 4 minus 3 okay and it will be 2 raised to the power 3 by 4 minus 3.

02:24 Minus 3 can be written as 12 by 4.

02:27 And it will be minus 9 by 4...

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