/*! 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 71 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 71

Perform the indicated operations: \(\left(7 \cdot 10^{5}\right)^{3} \cdot\left(3 \cdot 10^{-3}\right)^{4}\)

Short Answer

Expert verified
The short answer to the given expression \(\left(7 \cdot 10^{5}\right)^{3} \cdot\left(3 \cdot 10^{-3}\right)^{4}\) is \(\boxed{2.7783 \cdot 10^7}\).

Step by step solution

01

Calculate the cubes of 7 and 3

First, we need to find the cubes of 7 and 3: \(7^3 = 7 \cdot 7 \cdot 7 = 343\) \(3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81\)
02

Calculate the 3rd power of 10^鈦� and the 4th power of 10^-鲁

Next, we will find the third and fourth power of \(10^5\) and \(10^{-3}\), respectively: \( \left( 10^5 \right) ^3 = 10^{5 \cdot 3} = 10^{15}\) \( \left( 10^{-3} \right) ^4 = 10^{-3 \cdot 4} = 10^{-12}\)
03

Multiply the results

Now, we will multiply the calculated results from Steps 1 and 2 together: \((343 \cdot 10^{15}) \cdot (81 \cdot 10^{-12})\) When multiplying numbers in scientific notation, we can multiply the coefficients and then add the exponents of 10: \(343 \cdot 81 \cdot 10^{15} \cdot 10^{-12}\) \(343 \cdot 81 \cdot 10^{15 + (-12)}\)
04

Calculate the final result

Lastly, we need to calculate the product: \(343 \cdot 81 \cdot 10^3\) \(27783 \cdot 10^3\) Thus, the final result of the expression is: \(\boxed{2.7783 \cdot 10^7}\).

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!

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

Simplify (a) \(2^{3} \cdot 2^{2}\) (b) \(\mathrm{a}^{3} \cdot \mathrm{a}^{5}\) (c) \(x^{6} \cdot x^{4}\)

Evaluate \(\quad\) (a) \(8(-1 / 4)^{0}\) (b) \(6^{0}+(-6)^{0}\) (c) \(-7(-3)^{0}\) (d) \(9^{-1}\) (e) \(7^{-2}\)

Simplify the quotient \(\left(\mathrm{x}^{-2} \mathrm{y}^{4}\right)^{3} /(\mathrm{xy})^{-3}\)

Write the expression \(\left(\mathrm{x}+\mathrm{y}^{-1}\right)^{-1}\) without using negative exponents.

Determine the value of: \(\left(5^{3 / 4} 5^{2 / 3} 5^{-5 / 2} 5^{5 / 3}\right) /\left(5^{1 / 3} 5^{-5 / 2} 5^{7 / 4}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.