/*! 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 15 Compute the numbers. $$(.01)^{... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 15

Compute the numbers. $$(.01)^{-1}$$

Short Answer

Expert verified
100

Step by step solution

01

Understand the Problem

The goal is to find the value of \( (0.01)^{-1} \). This means raising 0.01 to the power of -1.
02

Recall the Negative Exponent Rule

A negative exponent means taking the reciprocal of the base. The rule is \( a^{-n} = \frac{1}{a^n} \).
03

Apply the Rule

Apply the negative exponent rule to the given problem: \( (0.01)^{-1} = \frac{1}{(0.01)^{1}} \). This simplifies to \( \frac{1}{0.01} \).
04

Simplify the Expression

Next, calculate the reciprocal of 0.01. The reciprocal of 0.01 is \( \frac{1}{0.01} = 100 \).
05

State the Final Answer

Thus, \( (0.01)^{-1} = 100 \).

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Key Concepts

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

Reciprocal
When we talk about the reciprocal of a number, we mean flipping the number over in a fraction. If you have any number, let's say 'a,' its reciprocal is given by \( \frac{1}{a} \). For example, the reciprocal of 2 is \( \frac{1}{2} \). Similarly, the reciprocal of 0.01 is \( \frac{1}{0.01} \), since 0.01 can be written as \( \frac{1}{100} \). When you flip it, you get 100. Therefore, understanding reciprocals is crucial for simplifying expressions, especially those involving negative exponents.
Simplifying Expressions
Simplifying expressions is the process of making a math problem easier to solve. When you see an expression like \( (0.01)^{-1} \), it might seem complex at first. However, by using the rules of exponents and reciprocals, you can make it easier. Here, step-by-step, we can:
  • Apply the negative exponent rule.
  • Take the reciprocal of the base.
  • Simplify the resulting fraction.
So, for \( (0.01)^{-1} \), we take the reciprocal of 0.01, which is 100, and simplify the expression. Simplifying makes math less intimidating and more manageable.
Exponentiation
Exponentiation refers to raising a number to a power. The power or exponent shows how many times the number (the base) is multiplied by itself. For instance, in \( a^n \), 'a' is the base, and 'n' is the exponent. In our problem, the base is 0.01, and the exponent is -1. Negative exponents have a unique rule: \( a^{-n} = \frac{1}{a^n} \). So, \( (0.01)^{-1} \) becomes \( \frac{1}{0.01^1} \), which simplifies to 100. Understanding exponentiation helps you handle both positive and negative powers, simplifying math problems effectively.

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