Use the Power Rule of Exponents to simplify the expression (788)6
The power rule of exponents states that when raising a power to another power, you multiply the exponents.
So, using the power rule of exponents, we can simplify the expression (788)^6 as follows:
(788)^6 = 7^(8*6)8^(8*6)8^(8*6)
Now, we can simplify the exponents:
(788)^6 = 7^(48)8^(48)8^(48)
Therefore, the expression (788)^6 simplifies to 7^(48)8^(48)8^(48).
Use the Power Rule of Exponents to simplify the expression (788)6.(1 point)
The power rule of exponents states that when raising a power to another power, you multiply the exponents.
So, using the power rule of exponents, we can simplify the expression (788)^6 as follows:
(788)^6 = 7^6 * 8^6 * 8^6
Now, we can simplify the exponents:
(788)^6 = 7^6 * (8 * 8)^6
(788)^6 = 7^6 * 64^6
Therefore, the expression (788)^6 simplifies to 7^6 * 64^6.
What exponent would make the two expressions equivalent: (16x)6=(1618)?(1 point)
To determine the exponent that would make the two expressions equivalent, we can equate the bases and solve for the exponent.
We have (16x)^6 = (16)^18.
To make the bases equal, we set the exponents equal to each other:
6 = 18.
This equation is not true, so there is no exponent that would make the two expressions equivalent.
To simplify the expression (788)6 using the Power Rule of Exponents, we can raise the base to the power of each exponent within the parentheses and then multiply the results.
First, let's break down the expression step by step:
1. Start with the base 788 and raise it to the power of 6.
(788)6 = 788^6
2. Apply the Power Rule of Exponents: Raise each factor within the base to the power of 6.
788^6 = (7 * 11 * 2^2)^6
We can break down the factor 788 into its prime factors, which are 7, 11, and 2^2.
3. Apply the Power Rule of Exponents to each factor within the parentheses:
(7 * 11 * 2^2)^6 = 7^6 * 11^6 * (2^2)^6
The Power Rule states that raising a product of factors to a power is the same as raising each factor to the power individually.
4. Simplify the exponents:
7^6 * 11^6 * (2^2)^6 = 7^6 * 11^6 * 2^(2 * 6)
In this case, we multiply the exponents because of the Power Rule.
5. Compute the values of each term with the simplified exponents:
7^6 = 117,649
11^6 = 1,771,561
2^(2 * 6) = 2^12 = 4,096
6. Substitute the computed values back into the expression:
117,649 * 1,771,561 * 4,096
Therefore, the simplified expression is 117,649 * 1,771,561 * 4,096.
To simplify the expression (788)6 using the Power Rule of Exponents, we need to raise 788 to the 6th power.
The Power Rule of Exponents states that when raising a number to an exponent, we multiply the base number by itself as many times as the exponent indicates.
(788)6 can be written as 788 * 788 * 788 * 788 * 788 * 788.
To simplify this expression, you can use a calculator or perform the multiplication manually.
By multiplying these numbers together, you will get the simplified form of (788)6.