To simplify the expression (6^2)^4, we can use the Power Rule of Exponents. The rule states that when we raise a power to a power, we multiply the exponents.
In this case, the base is 6, and the first exponent is 2. So, we raise 6 to the power of 2:
6^2 = 36
Now, we take this result and raise it to the power of 4. This means we need to multiply the exponent 2 by 4:
36^4 = 36^(2 * 4) = 36^8
Therefore, the simplified expression is 36^8.
Use the Power Rule of Exponents to simplify the expression (6^2)^4 .
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wrong
Apologies for the mistake. Let's correct it.
To simplify the expression (6^2)^4, we can use the Power Rule of Exponents. The rule states that when we raise a power to another power, we multiply the exponents.
In this case, the base is 6^2, and the exponent is 4. So, we need to raise 6^2 to the power of 4.
6^2 = 36
Now, we raise 36 to the power of 4:
36^4 = (6^2)^4 = 6^(2 * 4) = 6^8
Therefore, the simplified expression is 6^8.
To simplify the expression (6^2)^4, we can use the Power Rule of Exponents. The rule states that when we raise a power to another power, we multiply the exponents.
In this case, the base is 6^2, and the exponent is 4. So, we need to raise 6^2 to the power of 4.
6^2 = 36
Now, we raise 36 to the power of 4:
36^4 = (6^2)^4 = 6^(2 * 4) = 6^8
Therefore, the simplified expression is 6^8.
Use the Power Rule of Exponents to simplify the expression (73^4)^5 .
To simplify the expression (73^4)^5, we can use the Power Rule of Exponents. The rule states that when we raise a power to a power, we multiply the exponents.
In this case, the base is 73^4, and the exponent is 5. So, we need to raise 73^4 to the power of 5.
To find 73^4, we raise 73 to the power of 4:
73^4 = 285,768,253
Now, we raise this result to the power of 5:
(73^4)^5 = (285,768,253)^5 = 2,042,225,353,675,895,582,394,413,929,301,189,560,516,209
Therefore, the simplified expression is 2,042,225,353,675,895,582,394,413,929,301,189,560,516,209.
In this case, the base is 73^4, and the exponent is 5. So, we need to raise 73^4 to the power of 5.
To find 73^4, we raise 73 to the power of 4:
73^4 = 285,768,253
Now, we raise this result to the power of 5:
(73^4)^5 = (285,768,253)^5 = 2,042,225,353,675,895,582,394,413,929,301,189,560,516,209
Therefore, the simplified expression is 2,042,225,353,675,895,582,394,413,929,301,189,560,516,209.
simplify that
Apologies for the incorrect response.
To simplify the expression (73^4)^5, we can use the power rule of exponents. The rule states that when we raise a power to a power, we multiply the exponents.
To simplify, we multiply the exponents:
4 * 5 = 20
Therefore, the simplified expression is 73^20.
To simplify the expression (73^4)^5, we can use the power rule of exponents. The rule states that when we raise a power to a power, we multiply the exponents.
To simplify, we multiply the exponents:
4 * 5 = 20
Therefore, the simplified expression is 73^20.
Use the Power Rule of Exponents to simplify the expression (78^8)^6 .
To simplify the expression (78^8)^6, we can use the Power Rule of Exponents, which states that when we raise a power to another power, we multiply the exponents.
In this case, the base is 78^8, and the exponent is 6. Therefore, we need to raise 78^8 to the power of 6.
To simplify, we multiply the exponents:
8 * 6 = 48
Thus, the simplified expression is 78^48.
In this case, the base is 78^8, and the exponent is 6. Therefore, we need to raise 78^8 to the power of 6.
To simplify, we multiply the exponents:
8 * 6 = 48
Thus, the simplified expression is 78^48.
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) .(1 point)
To simplify the expression (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents, we can rewrite it as (12^3)⋅(12^3).
Now, using the Power Rule of Exponents, we can multiply the exponents:
3 + 3 = 6
Therefore, the simplified equivalent expression is 12^6.
Now, using the Power Rule of Exponents, we can multiply the exponents:
3 + 3 = 6
Therefore, the simplified equivalent expression is 12^6.
What exponent would make the two expressions equivalent: (16^x)^6=(16^18) ?
To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other and solve for x.
We have:
(16^x)^6 = 16^18
Applying the power rule of exponents, the exponent 6 can be distributed to both exponents inside the parentheses:
16^(6x) = 16^18
Since the bases are the same (16), we can equate the exponents:
6x = 18
Dividing both sides of the equation by 6, we get:
x = 3
Therefore, the exponent that would make the two expressions equivalent is x = 3.
We have:
(16^x)^6 = 16^18
Applying the power rule of exponents, the exponent 6 can be distributed to both exponents inside the parentheses:
16^(6x) = 16^18
Since the bases are the same (16), we can equate the exponents:
6x = 18
Dividing both sides of the equation by 6, we get:
x = 3
Therefore, the exponent that would make the two expressions equivalent is x = 3.
3 answers