7s over 5t to the negative 3rd power
2 to the negative 3rd power times X to the 2nd power times Z to the negative 7th power
7s to the zero power times T to the negative 5th power over 2 to the negative 1st power times M to the 2nd power
If you would please simplify these problems as much as you can.
Thanks
To simplify these expressions, we can use the rules of exponents. Here is how you can simplify each expression:
1. 7s over 5t to the negative 3rd power:
To simplify this, we can rewrite it as (7s) / (5t)^(-3). Using the rule (a^b) / (a^c) = a^(b-c), we can rewrite it as 7s / (5^(-3) * t^(-3)). Simplifying further, we get 7s * (5^3 / t^3) = 7s * (125 / t^3) = (875s) / (t^3).
2. 2 to the negative 3rd power times X to the 2nd power times Z to the negative 7th power:
To simplify this, we can rewrite it as (2^(-3) * x^2 * z^(-7)). Using the rule a^(-b) = 1 / (a^b), we get (1 / (2^3)) * x^2 * (1 / z^7) = (1/8) * x^2 * (1 / z^7) = x^2 / (8z^7).
3. 7s to the zero power times T to the negative 5th power over 2 to the negative 1st power times M to the 2nd power:
Any number raised to the power of zero is equal to 1. So, 7s^0 becomes 7 * 1 = 7. Now we have 7 * T^(-5) / (2^(-1) * M^2).
Simplifying further, we know that a^(-b) = 1 / (a^b). So T^(-5) becomes 1 / (T^5), and 2^(-1) becomes 1 / 2. Rewriting the expression, we have 7 / (T^5 * (1 / 2) * M^2).
Multiplying by the reciprocal of 1 / 2, we have 7 / (T^5 * (2 / 1) * M^2) = 7 / (T^5 * 2 * M^2) = 7 / (2T^5M^2).
So, the simplified expressions are:
1. (875s) / (t^3)
2. x^2 / (8z^7)
3. 7 / (2T^5M^2)
Sure! I'll simplify each of the expressions step-by-step for you:
1. Simplifying 7s over 5t to the negative 3rd power:
To simplify this expression, we can apply the rule that states a to the power of -n is equal to 1 divided by a to the power of n.
Therefore, 7s over 5t to the negative 3rd power can be rewritten as:
7s / (5t)^3
And then simplifying further, we get:
7s / (5^3 * t^3)
= 7s / (125t^3)
2. Simplifying 2 to the negative 3rd power times X to the 2nd power times Z to the negative 7th power:
To simplify this expression, we can apply the rule that states a to the power of -n is equal to 1 divided by a to the power of n.
Therefore, the expression becomes:
(1 / 2^3) * (x^2) * (1 / z^7)
Simplifying further, we get:
(1/8) * x^2 * (1 / z^7)
= x^2 / (8z^7)
3. Simplifying 7s to the zero power times T to the negative 5th power over 2 to the negative 1st power times M to the 2nd power:
Any number raised to the power of zero is equal to 1, so 7s to the zero power is equal to 1.
Applying the rule that states a to the power of -n is equal to 1 divided by a to the power of n, we get:
(1 * t^-5) / (2^-1 * m^2)
Simplifying further, we get:
t^-5 / (1/2 * m^2)
= 2t^-5 / m^2
Hope this helps! Let me know if you have any other questions.