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Write each of the following quotients with a single base. Do not simplify further. Write answers with positive exponents.
Write each of the following products with a single base. Do not simplify further. Write answers with positive exponents.
Write each of the following products with a single base. Do not simplify further. Write answers with positive exponents.
To simplify the power of a product of two exponential expressions, we can use the power of a product rule of exponents, which breaks up the power of a product of factors into the product of the powers of the factors. For instance, consider We begin by using the associative and commutative properties of multiplication to regroup the factors.
In other words,
For any real numbers and and any integer the power of a product rule of exponents states that
Simplify each of the following products as much as possible using the power of a product rule. Write answers with positive exponents.
Use the product and quotient rules and the new definitions to simplify each expression.
Simplify each of the following products as much as possible using the power of a product rule. Write answers with positive exponents.
To simplify the power of a quotient of two expressions, we can use the power of a quotient rule, which states that the power of a quotient of factors is the quotient of the powers of the factors. For example, let’s look at the following example.
Let’s rewrite the original problem differently and look at the result.
It appears from the last two steps that we can use the power of a product rule as a power of a quotient rule.
For any real numbers and and any integer the power of a quotient rule of exponents states that
Simplify each of the following quotients as much as possible using the power of a quotient rule. Write answers with positive exponents.
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