Using the Quotient Rule of Exponents, what is the exponent in an equivalent form of 7976 if the base is 7?(1 point)
The Quotient Rule of Exponents states that when dividing two exponential expressions with the same base, you subtract the exponents.
In this case, if the base is 7, we need to find the exponent in an equivalent form of 7976.
The exponent can be found by dividing 7976 by 7.
7976 ÷ 7 = 1139.4285714285714285714285714286 (rounded to the nearest decimal)
Therefore, the exponent in an equivalent form of 7976 if the base is 7 is approximately 1139.
The Quotient Rule of Exponents states that if we have a base raised to two exponents that are being divided, we can subtract the exponents.
In the given expression, 7976, the base is 7. To find the exponent in an equivalent form, we need to determine the difference between the exponents.
We can rewrite the expression as:
7^976
So, the exponent in the equivalent form is 976.
To find the exponent in an equivalent form of 7976 with a base of 7 using the Quotient Rule of Exponents, we can follow these steps:
Step 1: Write the number 7976 as a quotient of powers of 7.
Let's start by factoring 7976 into its prime factors.
7976 = 2^3 * 17 * 59
Step 2: Write the given number using the base 7 as a quotient of power with the same base.
7976 = (2^3 * 17 * 59) / 7^0
Step 3: Simplify the expression.
Since 7^0 is equal to 1, we can simplify further:
7976 = (2^3 * 17 * 59) / 1
Step 4: Apply the Quotient Rule of Exponents.
To apply the Quotient Rule of Exponents, we need to subtract the exponents when dividing powers with the same base. In this case, we have:
7976 = (2^3 * 17 * 59) / 1
= 2^(3-0) * 17^1 * 59^1
= 2^3 * 17 * 59
Therefore, the exponent in an equivalent form of 7976 with a base of 7 is 3.