x^-5 * x^7= x^5
can someone explain why and check if it is correct
X^-5 * X^7 = X^2
And the reason is because when u are multiplying with the same base, you add the exponents
thanks
To explain why the equation x^(-5) * x^7 = x^5 is correct, we need to understand the basic rules of exponents. The rule we will use here is that when multiplying two powers with the same base, you add their exponents.
In this equation, we have x^(-5) * x^7. Notice that both terms have the base x. Following the exponent rule, we add the exponents together, which gives us (-5 + 7). Simplifying this, we get x^2.
So the equation x^(-5) * x^7 simplifies to x^2. However, this does not match the equation x^5. Therefore, the original equation is not correct.
Correcting the equation: If we want to make it correct, we rewrite x^(-5) * x^7 as x^(-5 + 7), which simplifies to x^2. Thus, the correct equation would be x^2 = x^5.
To verify this equation, we can use an example. Let's take x = 2:
On the left side of the equation, we have 2^2 = 4.
On the right side, we have 2^5 = 32.
Since 4 is not equal to 32, it means that x^2 is not equal to x^5, making the equation x^2 = x^5 incorrect.
Hence, the original equation x^(-5) * x^7 = x^5 is not correct.