Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 98
Chapter 1, Problem 98

Simplify each expression. Write answers without negative exponents. Assume all variables represent positive real numbers. (z3/4)/(z5/4)(z-2)

Verified step by step guidance
1
Start by writing the expression clearly: \(\frac{z^{3/4}}{z^{5/4}} \cdot z^{-2}\).
Apply the property of exponents for division: \(\frac{a^m}{a^n} = a^{m-n}\). So, simplify \(\frac{z^{3/4}}{z^{5/4}}\) as \(z^{3/4 - 5/4} = z^{-2/4}\).
Simplify the exponent \(-2/4\) to \(-1/2\), so the expression becomes \(z^{-1/2} \cdot z^{-2}\).
Use the property of exponents for multiplication: \(a^m \cdot a^n = a^{m+n}\). Add the exponents: \(-1/2 + (-2) = -1/2 - 2\).
Combine the exponents to get \(z^{-5/2}\). Finally, rewrite the expression without negative exponents by using the rule \(a^{-m} = \frac{1}{a^m}\), so the simplified expression is \(\frac{1}{z^{5/2}}\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Laws of Exponents

The laws of exponents govern how to simplify expressions involving powers. Key rules include multiplying powers with the same base by adding exponents, dividing by subtracting exponents, and raising a power to another power by multiplying exponents. These rules allow simplification of complex expressions efficiently.
Recommended video:
Guided course
04:06
Rational Exponents

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, x^(-n) equals 1/x^n. Understanding this helps rewrite expressions without negative exponents, as required in the problem.
Recommended video:
Guided course
6:37
Zero and Negative Rules

Simplifying Expressions with Fractional Exponents

Fractional exponents represent roots and powers simultaneously, such as x^(m/n) meaning the n-th root of x raised to the m-th power. Simplifying expressions with fractional exponents involves applying exponent rules carefully while interpreting roots and powers correctly.
Recommended video:
Guided course
05:45
Radical Expressions with Fractions
Related Practice
Textbook Question

Evaluate each expression. 15÷5⋅4÷6−8−6−(−5)−8÷2\(\frac{15 \div 5 \cdot 4 \div 6 - 8}{-6 - (-5) - 8 \div 2}\)

2
views
Textbook Question

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [4(x2- 1)3 + 8x(x2-1)4] / [16(x2-1)3]

3
views
Textbook Question

Perform each division. See Examples 9 and 10. (4x3+9x2-10x-6)/(4x+1)

Textbook Question

Perform the indicated operations. Assume all variables represent positive real numbers. 372m2−532m2−318m23\(\sqrt{72m^2}\) - 5\(\sqrt{32m^2}\) - 3\(\sqrt{18m^2}\)

6
views
Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. (N ∪ R) ∩ M

Textbook Question

Add or subtract as indicated. 345.1 - 56.31