Power Rule of Exponents Practice
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Use the Power Rule of Exponents to simplify the expression (734)5.(1 point)
Use the Power Rule of Exponents to simplify the expression (788)6.(1 point)
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12).(1 point)
What exponent would make the two expressions equivalent: (16x)6=(1618)?(1 point)
what is the correct answer to each of these
1. (734)5 = 7320
2. (788)6 = 7836
3. (12⋅12⋅12)⋅(12⋅12⋅12) = 123⋅123 = 1728
4. (16x)6 = 1616x6 = 1618
The correct answers are:
1. 7320
2. 7836
3. 1728
4. 18
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To simplify the expressions and determine the correct answers, we can apply the Power Rule of Exponents.
1) Expression: (734)5
Using the Power Rule, we can distribute the exponent 5 to each factor inside parentheses:
(734)5 = 7^5 * 3^5 * 4^5
2) Expression: (788)6
By applying the Power Rule, we distribute the exponent 6 to each factor inside parentheses:
(788)6 = 7^6 * 8^6
3) Expression: (12⋅12⋅12)⋅(12⋅12⋅12)
We can simplify this expression by multiplying the factors inside each set of parentheses first:
(12⋅12⋅12)⋅(12⋅12⋅12) = 12^3 * 12^3
Using the Power Rule, we add the exponents of the same bases when multiplying:
= 12^(3+3)
= 12^6
4) Equating the expressions (16x)6 = (1618), we need to find the exponent that would make them equivalent.
Using the Power Rule, we can multiply the exponents of the same base:
6 = 18
Answer:
1) The simplified expression is 7^5 * 3^5 * 4^5.
2) The simplified expression is 7^6 * 8^6.
3) The simplified expression is 12^6.
4) The exponent that would make the expressions equivalent is 18.
To simplify expressions using the Power Rule of Exponents, remember that the rule states that when you raise the power of a base to another power, you multiply the exponents. Here's how to solve each question:
1. (734)5
To simplify this expression, raise each term inside the parentheses to the 5th power:
7^5 * 3^5 * 4^5
The result is:
16807 * 243 * 1024
2. (788)6
Similarly, raise each term inside the parentheses to the 6th power:
7^6 * 8^6 * 8^6
The result is:
117649 * 262144 * 262144
3. (12⋅12⋅12)⋅(12⋅12⋅12)
Multiply the terms inside each set of parentheses first:
(12^3) * (12^3)
Then apply the Power Rule of Exponents by multiplying the exponents:
12^(3+3)
Simplifying further, 3+3=6, so the expression reduces to:
12^6
4. (16x)6=(1618)
To make the two expressions equivalent, the exponents must be the same.
Set the exponents equal to each other:
6 = 16
This equation has no solution. The exponents cannot be equal in this case.
Now, I cannot provide the "correct" answers for each question as the calculation results depend on the specific values of the terms given in the original expressions. Please substitute the corresponding values and perform the calculations for the correct answers.