Use the Product Rule of Exponents to simplify the expression 75 ⋅72.(1 point)
The product rule of exponents states that when multiplying two exponential expressions with the same base, you can add the exponents.
In this case, we have 75 and 72 as the exponential expressions and they both have a base of 7. So, applying the product rule of exponents, the expression can be simplified as:
75 ⋅ 72 = 7^5 ⋅ 7^2
To simplify this further, we add the exponents:
7^5 ⋅ 7^2 = 7^(5+2) = 7^7
Therefore, the simplified expression is 7^7.
Find the numerical equivalent of 72⋅73(1 point)
To simplify the expression 75 ⋅ 72 using the Product Rule of Exponents, we add the exponents of the base when multiplying powers.
The expression can be written as (7^5) ⋅ (7^2).
Applying the Product Rule, we add the exponents: 7^(5+2).
This simplifies to 7^7.
Hence, the simplified expression is 7^7.
To simplify the expression 75 ⋅ 72 using the Product Rule of Exponents, we need to know the exponent rules. The Product Rule of Exponents states that when multiplying exponential expressions with the same base, you add the exponents.
In this case, we have 75 ⋅ 72, which can be rewritten using exponents as (7^2 ⋅ 5^1) ⋅ (7^2 ⋅ 2^3).
Now, let's apply the Product Rule of Exponents. For the first part, we multiply the bases, 7^2 ⋅ 7^2, which follows the rule of adding the exponents: 7^(2+2) = 7^4.
Next, we multiply the second part, 5^1 ⋅ 2^3, which doesn't have the same bases, so we can't apply the Product Rule of Exponents. Instead, we simply calculate the product: 5^1 ⋅ 2^3 = 5 ⋅ 8 = 40.
Now, we have 7^4 ⋅ 40, which cannot be simplified further because the bases are different.
So, the simplified expression using the Product Rule of Exponents is 7^4 ⋅ 40.