Use the power rule of exponents to simplify the expression (73⁴)⁵.
To simplify the expression using the power rule of exponents, we multiply the exponents together.
The power rule states that (a^m)^n = a^(m*n).
So, (73⁴)⁵ = 73^(4*5) = 73^20.
Therefore, the simplified expression is 73^20.
Use the power rule of exponents to simplify the expression (78⁸)⁶.
To simplify the expression using the power rule of exponents, we multiply the exponents together.
The power rule states that (a^m)^n = a^(m*n).
So, (78⁸)⁶ = 78^(8*6) = 78^48.
Therefore, 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).
To simplify the expression, we can combine the terms inside the parenthesis using the power rule of exponents.
We have (12•12•12) • (12•12•12) which can be written as 12^3 • 12^3.
Using the power rule of exponents, we can add the exponents when multiplying two numbers with the same base.
So, 12^3 • 12^3 = 12^(3+3) = 12^6.
Therefore, a simplified equivalent expression of (12•12•12) • (12•12•12) is 12^6.
What exponent would make the two expressions equivalent: (16x)⁶=(16¹⁸)?
To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other:
(16x)⁶ = (16¹⁸)
Since the bases are the same (16), we can set the exponents equal to each other:
6 = 18
However, this leads to a contradiction since 6 and 18 are not equal.
Therefore, there is no exponent that would make the two expressions equivalent.
What exponent would make the two expressions equivalent: (16^x)⁶=(16¹⁸)?
To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other:
(16^x)⁶ = (16¹⁸)
Since the bases are the same (16), we can set the exponents equal to each other:
6x = 18
To solve for x, we divide both sides of the equation by 6:
x = 18/6
Simplifying, we get:
x = 3
Therefore, an exponent of 3 would make the two expressions equivalent: (16^3)⁶=(16¹⁸).
To simplify the expression (73⁴)⁵ using the power rule of exponents, we need to raise the base (73⁴) to the power of the outside exponent (5). The power rule of exponents states that when we have an exponent raised to another exponent, we multiply the exponents.
In this case, we have (73⁴)⁵. We can rewrite (73⁴) as (73 × 73 × 73 × 73) and raise it to the power of 5.
To apply the power rule of exponents, we multiply the exponents. So, we have (73⁴)⁵ = 73^(4 × 5).
Now, we can simplify further by multiplying 4 and 5. 4 × 5 = 20. So, we have 73^(20).
Therefore, the simplified expression is 73^(20).