# What is the power of a product property?

Space and AstronomyThe Power of a Product Property states that **If a term is being raised to an exponent, you can distribute the exponent to each factor**.

Contents:

## What is an example of power of products property?

Video quote: *So by the power of a product property I'm multiplying lots of things together and that I'm cubing the entire quantity. So I can just cube each factor. So this equals four cubed multiplied by W squared*

## How do you find the power of a product property?

To find a power of a product, **find the power of each factor and then multiply**. In general, (ab)m=am⋅bm. am⋅bm=(ab)m. In other words, you can keep the exponent the same and multiply the bases.

## What does power of a product mean?

We use the power of a product rule **when there are more than one variables being multiplied together and raised to a power**. The power of a product rule tells us that we can simplify a power of a power by multiplying the exponents and keeping the same base.

## What is an example of a power of a product?

Example: Power of a Product With a Variable and Constant

**Simplify (8x) ^{4}**. The base is a product of a constant and a variable. Raise each by the given exponent.

## How do you use the power of a power property?

This is an example of the product of powers property tells us that when you multiply powers with the same base you just have to add the exponents. This is called the power of a power property and says that **to find a power of a power you just have to multiply the exponents**.

## When should you use product of powers property?

**When you are multiplying like terms with exponents**, use the product of powers rule as a shortcut to finding the answer. It states that when you are multiplying two terms that have the same base, just add their exponents to find your answer.

## How do you explain the product rule of exponents?

The product rule states that **if two factors raised to an exponent are being multiplied together, and they have the same base, we can add the exponents**. In this example, x and x 3 are our two factors.

## What is the product of powers formula?

Video quote: *Then if you take a and raise it to the M power and multiply that by a raised to the N power. The answer will be a raised to the power the sum of the exponents M plus N let's try some examples.*

## What is the product in exponents?

The Product of Powers Property states **when we multiply two powers with the same base, we add the exponents**. In this case, the exponents are 2 and 5.

## What is the product rule in law?

The Product Rule says that **the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function**.

## How do you write a product as a single power?

Video quote: *So the rule is whenever you are multiplying with the same base exponents. Get added when you divide they get subtracted.*

## What are the properties of exponent?

**Properties of Exponents**

- Law of Product: a
^{m}× a^{n}= a^{m}^{+}^{n} - Law of Quotient: a
^{m}/a^{n}= a^{m-n} - Law of Zero Exponent: a
^{0}= 1. - Law of Negative Exponent: a
^{–}^{m}= 1/a^{m} - Law of Power of a Power: (a
^{m})^{n}= a^{mn} - Law of Power of a Product: (ab)
^{m}= a^{m}b^{m} - Law of Power of a Quotient: (a/b)
^{m}= a^{m}/b^{m}

## What is a exponent power?

**An expression that represents repeated multiplication of the same factor** is called a power. The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor. 3^{1}. 3 to the first power.

## How do you simplify a product of powers?

To simplify a power of a power, you **multiply the exponents, keeping the base the same**. For example, (2^{3})^{5} = 2^{15}. For any positive number x and integers a and b: (x^{a})^{b}= x^{a}^{·} ^{b}. Simplify.

## What is the product property of square roots?

The Product Property of Square Roots states that **the square root of a product is equal to the product of the square roots of each of the factors**.

## What is the product of property?

The Product of Powers Property states that **when multiplying two exponents with the same base, you can add the exponents and keep the base**.

## What is the product property of logarithms?

The product rule: log b ( M N ) = log b ( M ) + log b ( N ) \log_b(MN)=\log_b(M)+\log_b(N) logb(MN)=logb(M)+logb(N) This property says that **the logarithm of a product is the sum of the logs of its factors**.

## What is product property math?

The product property of square roots is really helpful when you’re simplifying radicals. This property **lets you take a square root of a product of numbers and break up the radical into the product of separate square roots**.

## How do you calculate the power of a power?

Video quote: *When you have a power to the power all you need to do is multiply the powers. So in this particular example. It's three times four what do you do you multiply.*

## How do you raise a product to a power?

When raising a base with a power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent. When raising a product to a power, **distribute the power to each factor**.

## Is the product multiplication or addition?

Lesson Summary

**The product is the answer to a multiplication problem**. You can find a product by a process called repeated addition, which is to say, by adding together the number of groups in the problem.

## What operation is product?

A product is the result of carrying out the mathematical operation of multiplication. When you **multiply numbers together**, you get their product.

## How do you solve a product?

Video quote: *So I'm doing x times negative 3 always remember to look at that sign x times negative 3 which is negative 3x. Now I'm doing my inner term so the two terms that are in the middle. So I'm doing 4.*

## What is the product a 3 15a?

What is the product of a-3/15a * 5/a-3? The product is **1/3a**. What is the solution to the equation 3/2 = 3/2x – 6/5x? The solution to the equation is x=1/5.

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