Math Problem Statement

Problems related to exponents, simplifying powers, and calculating the volume of a cube based on side length.

Solution

Let's go through the problems you've circled from the image:

Write using an exponent:

  1. 222222 \cdot 2 \cdot 2 \cdot 2 \cdot 2
  • This can be written as 252^5.
  1. 77777 \cdot 7 \cdot 7 \cdot 7
  • This can be written as 747^4.

Simplify:

  1. 92=819^2 = 81

  2. (4)3=64(-4)^3 = -64

Volume of the sugar cube:

  1. The formula for the volume of a cube is V=s3V = s^3, where ss is the side length. Here, s=0.6s = 0.6 inches.
  • V=(0.6)3=0.216in3V = (0.6)^3 = 0.216 \, \text{in}^3

Let me know if you'd like further clarifications or explanations! Here's a set of related questions for practice:

  1. What is 353^5?
  2. Simplify (5)3(-5)^3.
  3. Find the volume of a cube with a side length of 1.2 inches.
  4. Simplify (2)4(-2)^4.
  5. Write 10101010101010 \cdot 10 \cdot 10 \cdot 10 \cdot 10 \cdot 10 using exponents.

Tip: When simplifying powers, remember that a negative base raised to an odd exponent stays negative, but to an even exponent, it becomes positive!

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Math Problem Analysis

Mathematical Concepts

Exponents
Powers
Volume of a Cube

Formulas

Exponentiation: a^n
Volume of a cube: V = s^3

Theorems

Properties of Exponents: a^m * a^n = a^(m+n), (a^m)^n = a^(mn)
Cubic Volume Formula

Suitable Grade Level

Grades 6-8