5^-6 x 5^? = 5^12
We can write this equation as an exponential equation:
5^-6 x 5^x = 5^12
To solve for x, we can use the property of exponents that states: a^m x a^n = a^(m+n)
Using this property, we can combine the bases of 5:
5^-6 x 5^x = 5^(12+6)
Now, we have the same base on both sides of the equation, which means the exponents must be equal:
-x + 6 = 12 + 6
Simplifying the right side:
-x + 6 = 18
Subtracting 6 from both sides:
-x = 18 - 6
-x = 12
To solve for x, we can multiply both sides of the equation by -1, to get:
x = -12
Therefore, x = -12.
x^3 * x^? = x^15
We can simplify the equation using the property of exponents that states: x^m * x^n = x^(m+n).
Using this property, we can rewrite the equation as:
x^3 * x^a = x^15
Now, we have the same base on both sides of the equation, which means the exponents must be equal:
3 + a = 15
Subtracting 3 from both sides:
a = 15 - 3
a = 12
Therefore, the missing exponent (represented by "?") is 12.
2^2 * 2^? = 2^13
We can simplify the equation using the property of exponents that states: a^m * a^n = a^(m+n).
Using this property, we can rewrite the equation as:
2^2 * 2^a = 2^13
Now, we have the same base on both sides of the equation, which means the exponents must be equal:
2 + a = 13
Subtracting 2 from both sides:
a = 13 - 2
a = 11
Therefore, the missing exponent (represented by "?") is 11.
simplify 8^18/8^-2
When dividing two terms with the same base, we can use the property of exponents that states a^m / a^n = a^(m - n).
Using this property, we can rewrite the expression as:
8^18 / 8^-2 = 8^(18 - (-2))
Simplifying the exponent:
= 8^(18 + 2)
= 8^20
Therefore, 8^18 / 8^-2 simplifies to 8^20.
z^?/z^4 = z^16
Using the property of exponents that states a^m / a^n = a^(m - n), we can rewrite the expression as:
z^? / z^4 = z^(? - 4)
According to the given equation, this should be equal to z^16:
z^(? - 4) = z^16
To solve for the missing exponent, we can equate the exponents:
? - 4 = 16
Adding 4 to both sides:
? = 20
Therefore, the missing exponent (represented by "?") is 20.