The equation x^4 . x^a = x^12 can be solved by using the properties of exponents. When multiplying two numbers with the same base, you add the exponents. Using this property, the equation becomes x^(4+a) = x^12.
Since the bases are the same, we can set the exponents equal to each other: 4+a = 12.
Now, we can solve for a:
a = 12 - 4
a = 8.
Therefore, the value of a is 8.
x^4 . x^a = x^12
17 answers
y^b/y^5 = y^2
The equation y^b/y^5 = y^2 can be simplified by using the quotient rule for exponents. According to the quotient rule, when dividing two numbers with the same base, you subtract the exponents. So, the equation becomes y^(b-5) = y^2.
Since the bases are the same, we can set the exponents equal to each other: b-5 = 2.
Now, we can solve for b:
b = 2 + 5
b = 7.
Therefore, the value of b is 7.
Since the bases are the same, we can set the exponents equal to each other: b-5 = 2.
Now, we can solve for b:
b = 2 + 5
b = 7.
Therefore, the value of b is 7.
y^b/
y^5 = y^2
y^5 = y^2
To solve the equation y^b/y^5 = y^2, we can use the quotient rule for exponents. According to the rule, when dividing two numbers with the same base, you subtract the exponents.
So, the left side of the equation becomes y^(b-5).
To make the equation true, we need to have y^(b-5) equal to y^2. This means that the exponents must be equal.
Therefore, b - 5 = 2.
We can solve for b by adding 5 to both sides:
b = 2 + 5 = 7.
Thus, the value of b is 7.
So, the left side of the equation becomes y^(b-5).
To make the equation true, we need to have y^(b-5) equal to y^2. This means that the exponents must be equal.
Therefore, b - 5 = 2.
We can solve for b by adding 5 to both sides:
b = 2 + 5 = 7.
Thus, the value of b is 7.
3^c = 1/27
In order to solve the equation 3^c = 1/27, we can rewrite 1/27 as a power of 3.
1/27 = 3^(-3)
So, the equation becomes 3^c = 3^(-3).
Since the bases are the same, we can equate the exponents:
c = -3
Therefore, the value of c is -3.
1/27 = 3^(-3)
So, the equation becomes 3^c = 3^(-3).
Since the bases are the same, we can equate the exponents:
c = -3
Therefore, the value of c is -3.
(m^3)^2 = m^d
To solve the equation (m^3)^2 = m^d, we can simplify the left side by applying the power of a power rule. The rule states that when raising a power to another power, you multiply the exponents.
(m^3)^2 = m^(3*2) = m^6
So, the equation becomes m^6 = m^d.
Now, we can equate the exponents:
6 = d
Therefore, the value of d is 6.
(m^3)^2 = m^(3*2) = m^6
So, the equation becomes m^6 = m^d.
Now, we can equate the exponents:
6 = d
Therefore, the value of d is 6.
7^0 = e
Actually, \( 7^0 = 1 \) rather than \( e \). Any number to the power of 0 is defined as 1.
7^0 = e
answer
answer
I apologize for the confusion. The correct statement is \(7^0 = 1\), not \(7^0 = e\). In general, any number raised to the power of 0 is equal to 1.
7^0 = 1
Yes, you are correct. 7^0 is equal to 1.
4^-2 . 4^9 . 4^-5 = 4^f
To solve this equation, we can use the properties of exponents. When multiplying numbers with the same base, you add the exponents.
Using this property, the equation becomes:
4^-2 . 4^9 . 4^-5 = 4^(-2 + 9 - 5) = 4^2.
Therefore, the value of f is 2.
Using this property, the equation becomes:
4^-2 . 4^9 . 4^-5 = 4^(-2 + 9 - 5) = 4^2.
Therefore, the value of f is 2.