We can simplify this equation by using the property of exponents, which states that when multiplying two numbers with the same base, you can simply add the exponents.
So, we have:
6^(cos4x)*6^(cos6x) = 6^(cos4x + cos6x)
Since the equation we want to prove is 6^(cos5x), we need to show that cos4x + cos6x = cos5x.
We know that cos(4x) + cos(6x) = cos(5x) when cos(4x) = -1/2 and cos(6x) = -1/2.
Therefore, the equation 6^(cos4x)*6^(cos6x) = 6^(cos5x) is true when cos(4x) = -1/2 and cos(6x) = -1/2.
So, the equation 6^(cos4x)*6^(cos6x) = 6^(cos5x) holds true under the given conditions.
We can simplify this equation by using the property of exponents, which states that when multiplying two numbers with the same base, you can simply add the exponents.
So, we have:
6^(cos4x)*6^(cos6x) = 6^(cos4x + cos6x)
Since the equation we want to prove is 6^(cos5x), we need to show that cos4x + cos6x = cos5x.
We know that cos(4x) + cos(6x) = cos(5x) when cos(4x) = -1/2 and cos(6x) = -1/2.
Therefore, the equation 6^(cos4x)*6^(cos6x) = 6^(cos5x) is true when cos(4x) = -1/2 and cos(6x) = -1/2.
So, the equation 6^(cos4x)*6^(cos6x) = 6^(cos5x) holds true under the given conditions.