Question

The ____ of Powers property allows you to rewrite xa· xb as xa + b.

Answer 1

Answer:

The Product of Powers property allows you to rewrite $x^a\times x^b=x^{a+b}$.

Step-by-step explanation:

We are given that,

The property allows us to write, $x^a\times x^b=x^{a+b}$

It is required to know the corresponding property.

As, we see that,

The expression involves the product of terms having same base resulting in the addition of the powers.

So, we have that,

The corresponding property is 'Product of Powers'.

Hence, the complete statement is,

The Product of Powers property allows you to rewrite $x^a\times x^b=x^{a+b}$.

Answer 2

The product of the Powers property $\large{\boxed{\bold{x^a\times\:x^b=x^{a+b}}}$

Further explanation

In general, we are dealing with numbers that can have large or small numbers

This exponent number was originally used as a multiple product

Exponent numbers are usually used in scientific notation. Scientific notation is used to express very large / small numbers

Exponent notation is used to write the product of repeated numbers in a simple form.

The exponent form function is to simplify writing and mention of a number that has the same multiplication factors

Exponents Number Operations

• 1. Multiplication
• 2. division
• 3. addition
• 4. substraction

Exponents Number can be

• 1. positive integers
• 2. zero integers
• 3. negative integers

General properties of numbers:

• 1. aᵇ x aⁿ = aᵇ⁺ⁿ

• 2. aᵇ: aⁿ = aᵇ⁻ⁿ, a ≠ 0

• 3. a⁻ᵇ = 1 / aᵇ, a ≠ 0

• 4. (aᵇ) ⁿ = aᵇⁿ

aⁿ: rank number

Exponent numbers show multiplication of the same factor

In the exponent there are base numbers and exponents / power / indexs

the exponent is written as a small number to the right and above the base number

Example: 7³ = 7 × 7 × 7 = 343

At number 7³, number 7 is called base and 3 is called exponent / power

7³if stated in sentence:

7 to the third power "," 7 to the power 3 "or" 7 cubed "

Multiplication

If two exponents have the same base we can add the exponent

$x^a\:\times x^b = x^{a+b}$

Example

7²⋅7³ = 7² + 5 = 7 x 7

Division

If two exponents have the same base we can divide the exponent

$x^a\:\divided x^b = x^{a-b}$

So:

The product of the Powers property allows you to rewrite $x^a\:\times x^b = x^{a+b}$

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Keywords: exponent, base, multiplication