Using the product rule of exponents, what is an equivalent form of 8 to the power of 2 times 8 to the power of 6
To find an equivalent form for 8 to the power of 2 times 8 to the power of 6, we can apply the product rule of exponents, which states that:
a^m * a^n = a^(m + n)
Applying this rule to the given expression:
8^2 * 8^6 = 8^(2 + 6)
Simplifying further:
8^(2 + 6) = 8^8
Therefore, an equivalent form of 8 to the power of 2 times 8 to the power of 6 is 8^8.
Using the product rule of exponents, what is an equivalent formm of 2 to the power of 6 times 2 to the power of 3?
To find an equivalent form for 2 to the power of 6 times 2 to the power of 3, we can apply the product rule of exponents, which states that:
a^m * a^n = a^(m + n)
Applying this rule to the given expression:
2^6 * 2^3 = 2^(6 + 3)
Simplifying further:
2^(6 + 3) = 2^9
Therefore, an equivalent form of 2 to the power of 6 times 2 to the power of 3 is 2^9.
Apply the product rule of exponents to form an equivalent expression of 1^6 times 1^2 times 1^1
The product rule of exponents states that:
a^m * a^n = a^(m + n)
Applying this rule to the given expression:
1^6 * 1^2 * 1^1
We can simplify the expression by adding the exponents:
1^(6 + 2 + 1)
Therefore, an equivalent expression for 1^6 * 1^2 * 1^1 using the product rule of exponents is 1^9.
Using the product rule of exponents what is an equivalent form of (1/3)^6 times (1/3)^6
To find an equivalent form of (1/3)^6 times (1/3)^6 using the product rule of exponents, we can apply the rule which states:
(a^m) * (a^n) = a^(m + n)
Applying this rule to the given expression:
(1/3)^6 * (1/3)^6 = (1/3)^(6 + 6)
Simplifying further:
(1/3)^(6 + 6) = (1/3)^12
Therefore, an equivalent form of (1/3)^6 times (1/3)^6 using the product rule of exponents is (1/3)^12.
Using the product rule of exponents, what is the exponent of 7^2 times 7^3 in exponential simplest form?
To find the exponent of 7^2 times 7^3 using the product rule of exponents, we can apply the rule which states:
a^m * a^n = a^(m + n)
Applying this rule to the given expression:
7^2 * 7^3 = 7^(2 + 3)
Simplifying further:
7^(2 + 3) = 7^5
Therefore, the exponent of 7^2 times 7^3 in exponential simplest form is 5.
What is the exponent in an equivalet form to the expression 1^1 times 1^3 if the base is 1?
If the base is 1, any positive exponent will still result in a value of 1. Therefore, in an equivalent form to the expression 1^1 times 1^3 with a base of 1, the exponent can be any positive integer but it will not affect the value, which will still be 1.
Using the product rule of exponents, what is the exponent of (1/2)^2 times (1/2)^2 in exponential simplest form?
To find the exponent of (1/2)^2 times (1/2)^2 using the product rule of exponents, we can apply the rule which states:
(a^m) * (a^n) = a^(m + n)
Applying this rule to the given expression:
(1/2)^2 * (1/2)^2 = (1/2)^(2 + 2)
Simplifying further:
(1/2)^(2 + 2) = (1/2)^4
Therefore, the exponent of (1/2)^2 times (1/2)^2 in exponential simplest form is 4.
Applying the product rule of exponents what is the exponent in the equivalent form of (5/6)^3 times (5/6)^10?
To find the exponent in the equivalent form of (5/6)^3 times (5/6)^10 using the product rule of exponents, we can apply the rule which states:
(a^m) * (a^n) = a^(m + n)
Applying this rule to the given expression:
(5/6)^3 * (5/6)^10 = (5/6)^(3 + 10)
Simplifying further:
(5/6)^(3 + 10) = (5/6)^13
Therefore, the exponent in the equivalent form of (5/6)^3 times (5/6)^10 using the product rule of exponents is 13.
Apply the product rule of exponents to solve and simplify 3^3 times 3^2 as an equivalent expression
To apply the product rule of exponents, we use the formula:
a^m * a^n = a^(m + n)
Applying this rule to the given expression:
3^3 * 3^2 = 3^(3 + 2)
Simplifying further:
3^(3 + 2) = 3^5
Therefore, an equivalent and simplified expression for 3^3 times 3^2 using the product rule of exponents is 3^5.