**Topic: Simplifying Expressions Involving Exponents**In the expression:$$\frac{\sqrt{a} \sqrt[3]{b}}{\sqrt{a^5 b}},$$when simplified, the exponent of $ a $ is [____] and the exponent of $ b $ is [____].**Explanation:**This problem involves simplifying an expression with roots and exponents. The given expression is a fraction with multiple root terms. To solve for the exponents of $ a $ and $ b $ once simplified, the rules of exponents and roots will be applied.**Steps to Simplify:**1. **Rewrite the Roots as Exponents:** - $\sqrt{a}$ can be written as $a^{1/2}$. - $\sqrt[3]{b}$ can be written as $b^{1/3}$. - $\sqrt{a^5 b}$ can be written as $(a^5 b)^{1/2} = a^{5/2} b^{1/2}$.2. **Combine the Exponent Terms:** - The numerator becomes $a^{1/2} b^{1/3}$. - The denominator is $a^{5/2} b^{1/2}$.3. **Subtract Exponents in the Denominator from the Numerator:** - $a$'s exponent in the numerator is $1/2$ and in the denominator is $5/2$. - $1/2 - 5/2 = -2$. - $b$'s exponent in the numerator is $1/3$ and in the denominator is $1/2$. - $1/3 - 1/2 = -1/6$.4. **Final Simplified Exponents:** - The exponent of $a$ is $-2$. - The exponent of $b$ is $-1/6$.Using this information, fill in the blanks in the provided format.---**Educational Objectives:**- To strengthen understanding of exponent laws and transformations.- To practice breaking down complex fraction expressions with roots.- To reinforce simplification techniques involving exponents.

Name: **Topic: Simplifying Expressions Involving Exponents**In the expressi
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: **Topic: Simplifying Expressions Involving Exponents**In the expression:$$\frac{\sqrt{a} \sqrt[3]{b}}{\sqrt{a^5 b}},$$when simplified, the exponent of $ a $ is [____] and the exponent of $ b $ is [____].**Explanation:**This problem involves simp

Answered: Image /qna-images/answer/2a16536f-6017-4024-b5e3-037ce88be4ab.jpg

Answered: In the simplified form of the exponent…

Math

Calculus

In the simplified form of the exponent of a is Vab and the exponent of b is

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: Use scientific notation to perform the following operation. Write the answer in scientific notation.…

A: We say a number is written in scientific notation if it is written as a product of a number that is…

Q: Use the laws of exponents to complete the equivalent expression for 5.62x5.62x.

A: We know, a*a=a²

Q: Jacob At times, 6 x.10° cubic feet of water go over Niagara Falls every minute. There are 1, 440…

A: On solving, we get

Q: Write the expression using an exponent: The number of coins Jada will have on the eighth day, if…

A: We have to slove above questions or

Q: Fill in the blank with an appropriate word, phrase, or symbol. With the negative exponent rule, for…

Q: Simplify using only positive exponents: 42xy 5 4x²y -5 4xxy10 1 4x27 20 4z7

Q: Simplify and write all in positive exponents : (ab2)(a-2b3)9

Q: Simplify each expression using the properties for exponents. u29 (a) 915 (b) 95 (c) 10 (d) 103

Q: Fill in the blank with an appropriate word, phrase, or symbol. With the negative exponent rule, for…

Q: express each answer as a single power, e.g. 26, AND evaluate. Demonstrate understanding of the…

Q: In the seventh term of (a + b)11, the exponent on a is

A: (a+b)11 find the seventh term using this expansion formula…

Q: In exponents and scientific notations, how does 5v0 equal 5?

A: Formula aman=am-n

Q: In scientific notation, which numbers have positive exponents and which havenegative exponents?

A: A positive exponent indicates a large number and a negative exponent indicates a small number that…

Q: Simplify using only positive exponents: 4-²xy-5 4¹x²y-524 Z

Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

Topic Video

Question

**Topic: Simplifying Expressions Involving Exponents**

In the expression:

$$\frac{\sqrt{a} \sqrt[3]{b}}{\sqrt{a^5 b}},$$

when simplified, the exponent of $ a $ is [____] and the exponent of $ b $ is [____].

**Explanation:**
This problem involves simplifying an expression with roots and exponents. The given expression is a fraction with multiple root terms. To solve for the exponents of $ a $ and $ b $ once simplified, the rules of exponents and roots will be applied.

**Steps to Simplify:**

1. **Rewrite the Roots as Exponents:**
- $\sqrt{a}$ can be written as $a^{1/2}$.
- $\sqrt[3]{b}$ can be written as $b^{1/3}$.
- $\sqrt{a^5 b}$ can be written as $(a^5 b)^{1/2} = a^{5/2} b^{1/2}$.

2. **Combine the Exponent Terms:**
- The numerator becomes $a^{1/2} b^{1/3}$.
- The denominator is $a^{5/2} b^{1/2}$.

3. **Subtract Exponents in the Denominator from the Numerator:**
- $a$'s exponent in the numerator is $1/2$ and in the denominator is $5/2$.
- $1/2 - 5/2 = -2$.
- $b$'s exponent in the numerator is $1/3$ and in the denominator is $1/2$.
- $1/3 - 1/2 = -1/6$.

4. **Final Simplified Exponents:**
- The exponent of $a$ is $-2$.
- The exponent of $b$ is $-1/6$.

Using this information, fill in the blanks in the provided format.

---

**Educational Objectives:**
- To strengthen understanding of exponent laws and transformations.
- To practice breaking down complex fraction expressions with roots.
- To reinforce simplification techniques involving exponents.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Algebraic Operations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

a. Write the expression in radical form.
Write each expression without using exponents: (금)' (a) (b) 3x° (c) (3x)º 13 We will note the base and exponent in each case. Since each expression has an exponent that is zero, we will use the zero-exponent rule. If an expression contains a nonzero base raised to the 0 power, we can replace it with 1. 1 ; the exponent is 0. 13 (a) The base is %3D 13 3x0 = 3( O) (b) The base is x the exponent is 0. = 3 (c) (3x)º The base is 3x. The exponent is 0. Parts (b) and (c) show that 3x° + (3x)°. Write each expression without using exponents. (a) (-0.115)° (b) -9a°b
Identify the coefficient and exponent of the term -8w-2 Coefficient Exponent:
4x Simplify: x – 5 x – 6 4x2 + 21x + 15 (x – 5) (x + 6) 4x2 - 27x + 21 (z – 6) (x – 5) | 4x- 3 2x +1 4x2- 27x + 15 (z - 6) (x – 5) 3.