which exponent makes the statement true? 1/5^9=5 ?
1 / 5⁹ = 5⁻⁹
To determine which exponent makes the statement 1/5^9 = 5 true, we can follow these steps:
Step 1: Start with the equation 1/5^9 = 5.
Step 2: Simplify the equation by evaluating the exponent on the left side of the equation. 5^9 = 1953125.
Step 3: Rewrite the equation with the simplified value: 1/1953125 = 5.
Step 4: To isolate the variable, multiply both sides of the equation by 1953125: 1 = 5 * 1953125.
Step 5: Evaluate the right side of the equation: 5 * 1953125 = 9765625.
Step 6: The equation now becomes: 1 = 9765625.
Step 7: Since 1 is not equal to 9765625, we can conclude that there is no exponent that makes the statement 1/5^9 = 5 true.
Therefore, the original equation does not hold true with any exponent.
To determine the exponent that makes the statement true, we can rewrite the equation and solve for the exponent.
The given equation is: 1/5^9 = 5.
To isolate the exponent, we can reverse the operations.
First, we can multiply both sides of the equation by 5 to cancel out the fraction on the left side:
(1/5^9) * 5 = 5 * 5.
This simplifies to:
1/5^9 = 25.
Next, we can take the reciprocal of both sides to isolate 5^9:
5^9 = 1/25.
This can be written as:
5^9 = 5^(-2).
Now we can set the exponents equal to each other and solve for the unknown exponent:
9 = -2.
However, this equation is not possible, as a positive exponent cannot be equal to a negative exponent. Thus, there is no exponent that makes the statement true.