/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 Convert to expressions with rati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 21

Convert to expressions with rational exponents. \(\sqrt[7]{t}\)

Short Answer

Expert verified
t^{1/7}

Step by step solution

01

Understand the Radical Notation

The expression \(\backslash sqrt[7]{t}\) represents the 7th root of t. The index here is 7.
02

Convert Radical to Exponent

Radicals can be expressed using rational exponents. The general form is: \(\backslash sqrt[n]{x} = x^{1/n}\). For this problem, \(\backslash sqrt[7]{t}\) is equivalent to \(t^{1/7}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

radical notation
Radical notation involves expressing roots of numbers using the radical symbol (鈭�).
The number under the radical symbol is called the radicand. For instance, in \(\backslash sqrt[n]{x}\), 'x' is the radicand.
The small number above and to the left of the radical symbol is the index.
It shows the degree of the root.\(\backslash sqrt{7}{t}\) means the 7th root of t, where t is the radicand and 7 is the index.
exponents
Exponents are a way to express repeated multiplication of a number by itself.
For example, \( a^2 \) means multiplying 'a' by itself: \( a\cdot a \).
Rational exponents involve expressing roots as fractions.
For example, \( x^{1/2} \) is another way to write the square root of x.
The exponent 1/2 acts as the square root operator.
A rational exponent of 1/7, like in \( t^{1/7} \), means taking the 7th root of 't'.
7th root
The 7th root of a number means you need a value which, when multiplied by itself 7 times, gives the original number.
In mathematical terms, if \( a = b^{7} \), then b is called the 7th root of 'a'.
For instance, \( 2 \) is the 7th root of \( 128 \), since \( 2^{7} \) equals 128.
In the case of \( \sqrt[7]{t} \), it can be converted to \( t^{1/7} \).
This way, we use rational exponents to express roots more flexibly.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a calculator to evaluate the following trigonometric functions. $$ \sin (-2.04) $$

Solar Radiation. The annual radiation (in megajoules per square centimeter) for certain land areas of the northern hemisphere may be modeled with the equation \({ }^{19}\) \(R=0.339+0.808 \cos l \cos s-0.196 \sin l \sin s\) \(-0.482 \cos a \sin s\) In this equation, \(l\) is the latitude (between \(30^{\circ}\) and \(60^{\circ}\) ) and \(s\) is the slope of the ground (between \(0^{\circ}\) and \(60^{\circ}\) ). Also, \(a\) is the aspect, or the direction that the slope faces. For a slope facing due north, \(a=0^{\circ}\), and for a slope facing south, \(a=180^{\circ} .\) For a slope facing either east or west, \(a=90^{\circ}\). Find the annual radiation of south-facing land at \(30^{\circ}\) north latitude with a \(20^{\circ}\) slope.

Use a calculator to find the values of the following trigonometric functions. \(\csc 72^{\circ}\)

Sketch the following angles. \(2 \pi\)

Use a unit circle to compute the following trigonometric functions \(\cos (-5 \pi / 4)\)
See all solutions

Recommended explanations on Biology Textbooks

Ecosystems

Read Explanation

Cell Communication

Read Explanation

Plant Biology

Read Explanation

Biological Processes

Read Explanation

Chemistry of Life

Read Explanation

Cells

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.