Use the Product Rule of Exponents to simplify 510⋅55
To simplify 510⋅55 using the Product Rule of Exponents, we need to add the exponents of 5.
The product rule states that when multiplying two numbers with the same base, you can add their exponents.
In this case, 5 has an exponent of 10 and an exponent of 5, so we can add the exponents:
510⋅55 = 5(10+5) = 5^15
To simplify the expression 510⋅55 using the Product Rule of Exponents, we follow these steps:
Step 1: Identify the base of the exponents.
The base of the first exponent is 5, and the base of the second exponent is also 5.
Step 2: Apply the Product Rule of Exponents.
According to the Product Rule of Exponents, when multiplying two numbers with the same base, we add their exponents. Therefore, we add the exponents of 10 and 5.
Step 3: Calculate the resulting exponent.
The exponents are 10 and 5. Adding them together gives 10 + 5 = 15.
Step 4: Write the simplified expression.
The simplified expression is 5^15.
To simplify the expression 510⋅55 using the product rule of exponents, we need to remember that the rule states that when multiplying two numbers with the same base, we can add their exponents.
Let's break down the given expression step by step:
Step 1: Start with 510⋅55
Step 2: In 510, the base is 5, and the exponent is 10. In 55, the base is 5, and the exponent is 5.
Step 3: Apply the product rule of exponents by adding the exponents of the same base.
Adding the exponents 10 and 5 gives us 10 + 5 = 15.
So, the simplified expression is 515.
Therefore, 510⋅55 simplifies to 515.