Which expression is equivalent to (5^-1)^-2
1. 1
2. 25
3. 1/5
4. 125
The expression (5^-1)^-2 can be simplified by using the rule of exponentiation: (a^m)^n = a^(m*n).
In this case, we have (5^-1)^-2. The exponent -2 multiplied by the exponent -1 gives -2 * -1 = 2. So we have (5^2).
Therefore, the expression is equivalent to 25.
The answer is 2. 25.
To solve the expression (5^-1)^-2, we need to follow the exponent rules.
First, let's simplify the expression within the parentheses, which is 5^-1.
Recall that any positive number raised to the power of -1 is equal to its reciprocal.
Therefore, 5^-1 is equal to 1/5.
Now we have (1/5)^-2.
To simplify this, we apply the power of a fraction rule, which states that any fraction raised to a negative exponent can be rewritten as the reciprocal of the fraction raised to the positive exponent.
So, (1/5)^-2 is equal to 5^2/1, which is equal to 25.
Therefore, the expression (5^-1)^-2 is equivalent to 25.
The correct answer is 2. 25.
To find the value of the expression (5^-1)^-2, we need to apply the exponent rules.
Step 1: Simplify the expression inside the parentheses first.
Since 5^-1 means the reciprocal of 5 (1/5), the expression becomes (1/5)^-2.
Step 2: Apply the exponent rule for a negative exponent.
When a term with a negative exponent is raised to a negative exponent, we change the sign of the exponent and move the term to the opposite side of the fraction. So, (1/5)^-2 becomes (5/1)^2.
Step 3: Compute the value of the expression (5/1)^2.
(5/1)^2 is calculated by squaring both the numerator and denominator of the fraction. Therefore, (5/1)^2 is equal to (5^2)/(1^2), which simplifies to 25/1 or simply 25.
Therefore, the expression (5^-1)^-2 is equivalent to 25.
The correct answer is option 2. 25.