Tuesday, August 9, 2022

# Infinite Algebra 1 Properties Of Exponents

## Kuta Software Infinite Algebra 1 Answers

KutaSoftware: Algebra 1- Properties Of Exponents Easy Part 1

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Kuta software infinite algebra 1 properties of exponents. Your answer should contain only positive exponents. Free Algebra 1 Worksheets.

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## Algebra 1 Properties Of Exponents Worksheet

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## Multiplying Powers With The Same Exponents

For example: 3² × 2², 5³ × 7³We consider the product of 4² and 3², which have different bases, but the same exponents. 4² × 3² = × = 12 × 12= 12²Here, we observe that in 12², the base is the product of bases 4 and 3.

We consider,

4³ × 2³= × = × × = 8 × 8 × 8

We also have, 2³ × a³= × = × × = ³= ³

Similarly, we have, a³ × b³= × = × × = ³= ³

Note: In general, for any non-zero integer a, b. a × b=

a × b =

Note: Where m is any whole number.³ × ³= × = × × = ³= ³,

## An Introduction To Exponents

When it is 100, 29, or even 135000, it is easier to read these numbers as a whole. However, consider the number 294800000000, was this simple to read? Maybe yes, but somehow takes time to evaluate. But then, when the same number is denoted as 2948 × 108, it was quick and easy to say out. Now, this method of using powers to express a long set of natural numbers is called Exponents.

This module is focussed on giving you an introduction to exponents, along with a few examples and types.

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## A Gist About Negative Numbers With Examples

Similar to positive exponents, a negative number is equated by having the reciprocal of the positive value obtained from an expression. Say, that the base 6 has the negative power value of -2. This is symbolized as 6-2.

Now, calculate the digits value by moving the negative exponent at the denominator, i.e. reciprocal of the positive power. Hence it becomes 1/62 which is 1/36.

Here are 2 more examples of negative exponents.

• 4-3: 1/43 which is 1/64.

• 10-5: 1/105 upon simplification gives 100000.

• ## Simple Examples To Understand Exponents

KutaSoftware: Algebra 1- Properties Of Exponents Easy Part 3
• Base 10 and power 3 is denoted as 103. Now, you can find its value by multiplying 10 3 times , which is 10 × 10 × 10 = 1000.

• The number 23450000000 can be exponentially denoted as 2345 × 107.

• With an exponent value of 4 and the base as 2, i.e. 23, the natural number is obtained by multiplying 2 three times. Hence, the answer is 2 × 2 × 2 = 8.

• The base 1000 with its Index value 1 is represented as 10001. The simplification of this exponent is 1000 since the power value is only 1 and the base value remains unchanged.

• 716929 × 103 can be numerically expressed as 716929000.

Make sure to check the sign of both the base and exponent, as 2 negative signs will give you a positive value. And the odd count of negative exponents will give you a negative result. Again, consider the instance -103. Now the answer is -10 × -10 × -10 = -1000 and not simply 1000. However, in the case of -102, the answer is -10 × -10 = 100 .

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## Get Properties Of Exponents Worksheet Algebra 1 Answers From This Site

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## Get Algebra 1 Properties Of Exponents Worksheet Answers From Our Site

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## Four Major Forms Of Exponents

In the process of getting an introduction to exponents, we will now learn the 4 major types of Indices, subjected upon the value present as its power:

• Rational exponent – Square or Cube roots turn radical. The number is simplified by having the denominator of the exponent outside the root and keeping the base number as root, with its power as the numerator.

• Positive exponent – A number is simplified by multiplying its base with the number of times mentioned in its power.

• Negative exponent – The value is estimated by using 1 in its numerator and base, plus the exponent in its denominator.

• Zero exponent – The set does not even have to be calculated since any exponent with the value of 0 is equal to 1.

• ## Dividing Powers With The Same Base

For example: 3 ÷ 3¹, 2² ÷ 2¹, 5 ÷ 5³In division if the bases are same then we need to subtract the exponents. Consider the following: 2 ÷ 2 = \

= 2\

5 ÷ 5² = \

= = \

= 5\

10 ÷ 10³ = \

= 10\

7 ÷ 7 = \

= 7\

Let a be a non zero number, thena ÷ a³ = \

= a\

again, a³ ÷ a = \

= a\

Thus, in general, for any non-zero integer a, a ÷ a = \ = a\

Note 1: Where m and n are whole numbers and m > n a ÷ a = \ = a\

Note 2: Where m and n are whole numbers and m < n We can generalize that if a is a non-zero integer or a non-zero rational number and m and n are positive integers, such that m > n, then a ÷ a = a\ if m < n, then a ÷ a = \

Similarly, \^\) ÷ \^\) = \ \

For example:

1. 7\ ÷ 7 = \

= \ = 7\,

= 7²2. p ÷ p¹ = \

= p\,

= p3. 4 ÷ 4² = \

= \ = 4\,

= 4² 4. 10² ÷ 10 = \

= \ = 10\,

= 10\

5. 5³ ÷ 5¹= 5\

6. \

= 3\7. \

= \8. ) ÷ )

= )\= )³

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## Properties Of Logarithms Expanding Logarithms

Properties of Logarithms Expanding Logarithms What are the Properties of Logarithms? The properties of logarithms are very similar to the properties of exponents because as we have seen before every exponential equation can be written in logarithmic form and vice versa. … Rewrite any radicals using rational exponents .

## Algebra 1 Properties Of Exponents Worksheet Answers

KutaSoftware: Algebra 1- Properties Of Exponents Hard Part 3

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