/*! 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 14 Multiply and simplify. Leave the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 14

Multiply and simplify. Leave the answer in exponential notation. $$ t^{6} \cdot t^{0} $$

Short Answer

Expert verified
t^{6}

Step by step solution

01

Understand Exponent Rules

Recall the rule of multiplying powers with the same base: When multiplying like bases, add the exponents. For any base, the equation is \( a^{m} \times a^{n} = a^{m+n} \).
02

Apply the Zero Exponent Rule

Recall that any number raised to the power of zero equals one. Thus, \( t^{0} = 1 \).
03

Add the Exponents

Using the rule from Step 1, add the exponents: \( t^{6+0} \). This simplifies to \( t^{6} \).
04

Simplify

Since adding zero to any number does not change its value, \( t^{6} \) remains as \( t^{6} \).

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.

multiplying like bases
Multiplying like bases involves combining exponents from terms that share the same base. In this exercise, our terms are both based on 't': \( t^{6} \) and \( t^{0} \).

The rule to remember is simple: **add the exponents** when you multiply terms with the same base.

For example, if you have \( a^{m} \) and \( a^{n} \), their product is \( a^{m+n} \).

Therefore, in our situation: \( t^{6} \times t^{0} = t^{6+0} \). This will simplify to \( t^{6} \).

This rule helps us manage and simplify expressions efficiently without losing accuracy. Try applying this in your own exercises to see how it simplifies your computations.
zero exponent rule
The zero exponent rule is a handy and sometimes surprising rule in exponents. The rule states that any non-zero base raised to the power of zero equals one.

This means \( t^{0} = 1 \). So, applying this in our exercise, we see that \( t^{6} \times t^{0} \) can be read as \( t^{6} \times 1 \).

Why does this work? Think of it this way: if you divide a number by itself, except the number is non-zero, you always get 1. So mathematically, \( t^{n} / t^{n} = 1 \), hence \( t^{0} = 1 \).

This is a fundamental concept that comes up often in algebra and higher-level mathematics.
adding exponents
Adding exponents is a key skill when dealing with expressions that have the same base.

Remember the simple rule: when multiplying terms with the same base, add their exponents. For our exercise: \( t^{6} \times t^{0} \) translates to \( t^{6+0} \).

So, \( t^{6+0} = t^{6} \).
This rule is derived from the properties of exponents that allow us to rewrite multiplication of like bases as a single term with a combined exponent.

Practicing this rule with various bases and exponents will make it second nature. It helps in streamlining calculations and solving more complex algebraic expressions.

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 roster notation to write each set. The set of all odd natural numbers

Divide. $$ \left(-\frac{2}{7}\right) \div(-1) $$

Find an equivalent expression by factoring. $$ 5 d+30 $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{N} \subseteq W $$

Tico's scores on four tests are \(83,91\) \(78,\) and \(81 .\) How many points above his current average must Tico score on the next test in order to raise his average 2 points?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.