(2^-5)^5
To simplify the expression (2^-5)^5, we can first simplify the exponent of 2.
The exponent of a power raised to another power is found by multiplying the exponents. Therefore, (-5) * 5 = -25.
So, (2^-5)^5 can be written as 2^(-25).
Now, we can rewrite 2^(-25) as the reciprocal of 2^25.
Since 2^25 is a positive number (as any number raised to a positive exponent is positive), the reciprocal will also be positive.
Therefore, (2^-5)^5 is equal to 1/2^25.
(y^-5)-2
To simplify the expression (y^-5)^-2, we can apply the rule for negative exponents.
The rule states that for any non-zero number a and any integer n:
(a^-n) = 1 / (a^n)
Using this rule, we can rewrite (y^-5)^-2 as 1 / (y^(-5 * -2)).
Since -5 * -2 equals 10, we can further simplify the expression to 1 / (y^10), where the negative exponent has become positive.
Therefore, (y^-5)^-2 simplifies to 1 / (y^10).
simplify
I apologize, but you haven't mentioned the specific expression that you would like me to simplify. Could you please provide me with more information?
To simplify the expression (2^-5)^5, we start by applying the exponent rule which states that when a power is raised to another power, we multiply the exponents.
In this case, we have (2^-5)^5.
When raising a power to another power, we multiply the exponents. So, we have:
2^(-5 × 5)
Multiplying -5 by 5 gives us -25, so we have:
2^-25
Now, let's simplify this further. We know that a negative exponent indicates a reciprocal, so:
2^-25 = 1/2^25
Therefore, the expression (2^-5)^5 simplifies to 1/2^25.
To calculate the value of (2^-5)^5, we can follow these steps:
Step 1: Evaluate the exponent of 2^-5. In this case, we raise 2 to the power of -5.
2^-5 = 1 / 2^5
Step 2: Simplify 2^5.
2^5 = 2 * 2 * 2 * 2 * 2 = 32
Step 3: Substitute the simplified value back into the original expression.
(2^-5)^5 = (1 / 2^5)^5
Step 4: Apply the power of a power rule. To raise a power to another power, multiply the exponents.
(1 / 2^5)^5 = 1^5 / (2^5)^5
Step 5: Simplify 1^5 and (2^5)^5.
1^5 = 1
(2^5)^5 = 32^5
Step 6: Evaluate 32^5.
32^5 = 32 * 32 * 32 * 32 * 32 = 33,554,432
Step 7: Substitute the simplified values back into the expression.
(2^-5)^5 = 1 / (32^5)
Therefore, the value of (2^-5)^5 is 1 / 33,554,432.