5 Problems - SHOW ALL WORK!
x^-1/x^2=
(x^-2)^-1
x^-5*x^4
1/x^-2*x^4
Compare 10^2 to 10^-2
1) Simplify x^-1/x^2:
To simplify this expression, we will use the property of negative exponents which states that x^-n = 1/x^n. We can rewrite x^-1 as 1/x, so:
x^-1/x^2 = 1/x / x^2
To divide by x^2, we can use the property of division which states that a/b = a * 1/b. So:
1/x / x^2 = 1/x * 1/x^2
Using the property of exponents, x^-n = 1/x^n, we can rewrite this as:
= 1/x * 1/(x^2)
= 1/(x * x^2)
= 1/(x^3)
Therefore, x^-1/x^2 simplifies to 1/(x^3).
2) Simplify (x^-2)^-1:
To simplify this expression, we will use the property of negative exponents. We know that (a^-n)^m = a^(-n * m). So:
(x^-2)^-1 = x^(-2 * -1)
When multiplying two negative exponents, they cancel out and become positive. Therefore:
x^(-2 * -1) = x^2
So, (x^-2)^-1 simplifies to x^2.
3) Simplify x^-5 * x^4:
When multiplying two exponents with the same base, we can add their exponents. So:
x^-5 * x^4 = x^(-5 + 4)
= x^-1
= 1/x
Therefore, x^-5 * x^4 simplifies to 1/x.
4) Simplify 1/x^-2 * x^4:
When dividing two exponents with the same base, we can subtract their exponents. So:
1/x^-2 * x^4 = 1/x^(-2 - 4)
= 1/x^-6
= x^6
Therefore, 1/x^-2 * x^4 simplifies to x^6.
5) Compare 10^2 to 10^-2:
To compare these two numbers, we can write them in decimal form. 10^2 is equal to 100, and 10^-2 is equal to 1/10^2, which is equal to 1/100 or 0.01.
So, 10^2 is greater than 10^-2.