Using the Product Rule of Exponents, what is an equivalent form of 8^2⋅8^6
The Product Rule of Exponents states that when multiplying two powers with the same base, you add the exponents.
In the given expression, 8^2 ⋅ 8^6, the base is 8. Therefore, by applying the product rule of exponents, we can add the exponents:
8^2 ⋅ 8^6 = 8^(2+6)
Simplifying the exponent, we have:
8^(2+6) = 8^8
Therefore, an equivalent form of 8^2 ⋅ 8^6 is 8^8.
To simplify the expression using the Product Rule of Exponents, we can add the exponents when the base is the same. The Product Rule states that for any real numbers a and b, and any positive integer n, (a^n)(a^m) = a^(n+m).
In this case, we have 8^2 ⋅ 8^6. Since the base is the same (8), we can add the exponents:
8^2 ⋅ 8^6 = 8^(2+6)
Simplifying the exponent, we have:
8^(2+6) = 8^8
Therefore, an equivalent form of 8^2 ⋅ 8^6 is 8^8.
To simplify the expression 8^2 * 8^6 using the Product Rule of Exponents, we can add the exponents since the base is the same. The rule states that for any number a raised to the power of m, multiplied by the same number a raised to the power of n, the result is a raised to the power of m+n.
Therefore, 8^2 * 8^6 = 8^(2+6) = 8^8.
So, an equivalent form of 8^2 * 8^6 is 8^8.
so the answer is 8^(2+6)?
Yes, that is correct.
Using the Product Rule of Exponents, what is an equivalent form of 2^6⋅2^3
The Product Rule of Exponents states that when multiplying two powers with the same base, you add the exponents.
In the given expression, 2^6 ⋅ 2^3, the base is 2. Therefore, by applying the product rule of exponents, we can add the exponents:
2^6 ⋅ 2^3 = 2^(6+3)
Simplifying the exponent, we have:
2^(6+3) = 2^9
Therefore, an equivalent form of 2^6 ⋅ 2^3 is 2^9.
Apply the Product Rule of Exponents to form an equivalent expression of 1^6⋅1^2⋅1^1
The Product Rule of Exponents states that when multiplying two powers with the same base, you add the exponents.
In the given expression, 1^6 ⋅ 1^2 ⋅ 1^1, the base is 1. Regardless of the exponent, any number raised to the power of 1 remains the same number. Therefore, we can simplify the expression as:
1^6 ⋅ 1^2 ⋅ 1^1 = 1 ⋅ 1 ⋅ 1
Since any number multiplied by 1 remains unchanged, we get:
1 ⋅ 1 ⋅ 1 = 1
Therefore, an equivalent form of 1^6 ⋅ 1^2 ⋅ 1^1 is simply 1.
Apply the Product Rule of Exponents to form an equivalent expression of 1^6⋅1^2⋅1^1 .(1 point)
Responses
112
1 superscript 12 baseline
13
1 cubed
113
1 superscript 13 baseline
19
1 superscript 9 baseline