What is an expression equivalent to 6^-5/3^-5
An expression equivalent to 6^-5/3^-5 is 3^5/6^5.
To find an expression equivalent to 6^-5/3^-5, we can rewrite it using the properties of exponentiation. Recall that for any non-zero real number a, a^(-n) is equivalent to 1/a^n.
Therefore, we can rewrite the expression as (1/6^5)/(1/3^5). Now, dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. So we can rewrite the expression as (1/6^5)*(3^5/1).
Now simplify each term separately. 6^5 means 6 multiplied by itself 5 times, which equals 7776. Similarly, 3^5 means 3 multiplied by itself 5 times, which equals 243.
Substituting these values back into the expression, we have (1/7776)*(243/1). Multiplying the numerators together and the denominators together, we get 243/7776.
Thus, an expression equivalent to 6^-5/3^-5 is 243/7776.
To simplify the expression 6^-5/3^-5, we can use the rule that states when dividing two numbers with the same base, we subtract the exponents. In this case, the base is 6 and the exponents are -5 and -5.
So, we can rewrite the expression as (6/3)^(-5-(-5)).
Now, the expression simplifies to (2)^0 because -5 - (-5) is equal to 0.
Any number raised to the power of 0 is always equal to 1. Therefore, the expression is equivalent to 1.