Your answer will be x • 4³ = 64x
When simplifying powers, the rule is that if you’re dividing two powers with the same base (in this case the base is 4), you need to subtract the powers. For example, 3³ ÷ 3² = 3 (which is 3^1).
Using this rule, we can see that 4^8 ÷ 4^5 = 4^(8-5) = 4³.
The x is on top of the fraction and we’re not dividing by an x, so it doesn’t change. Therefore your final answer is 64x.
I hope this helps!
Answer:
x = ±25
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
x² = 625
<u>Step 2: Solve for </u><em><u>x</u></em>
- Square root both sides: x = ±25
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
x = -25
- Substitute in <em>x</em>: (-25)² = 625
- Exponents: 625 = 625
Here we see that 625 does indeed equal 625.
∴ x = -25 is a solution to the equation.
x = 25
- Substitute in <em>x</em>: 25² = 625
- Exponents: 625 = 625
Here we see that 625 does indeed equal 625.
∴ x = 25 is a solution to the equation.
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In order to answer this, it would be useful to calculate the area of the cardboard and the circles. We do as follows:
Total area of cardboard = <span> 8.0 in. x 11.0 in = 88 in^2
Area of one circle = pi(r^2) = pi(0.5)^2 = 0.7854 in^2
Number of full circles = 88 / 0.7854 = 112.0451
Therefore, there will be 112 number of full circles. The percentage of waste is equal to:
% waste = (88 - 0.7854(112) / 88) x 100= 0.04%</span>
