c A negative exponent of an integer or a variable will be moved to the denominator and become positive.
D
d To simplify the given expression, use the Properties of Exponents.
A
a 1
B
b 20/x
C
c 5/t^3
D
d x^2y
Practice makes perfect
a To simplify the given expression we will use the Properties of Exponents. Recall that any number or expression with an exponent of 0 equals 1.
a^0=1
Thus, even though the product inside parentheses may look complicated, the whole given expression equals 1.
( - 2/3x^5y^(1/3))^0=1
b To simplify the given expression, we will use the Properties of Exponents. For this exercise, we will begin by rewriting a power with an exponent 12 as a square root of the base. Let's do it!
c We want to simplify the given expression. We can see that t has a negative exponent. When this is the case, the variable can be moved to the denominator and the exponent will become positive. Notice that the negative exponent is applied only to the variable t, not to 5.
a^(- n)= 1/a^n ⇒ t^(- 3)=1/t^3
Now, to simplify the expression completely we will substitute the obtained quotient into the given expression and multiply.
5 t^(- 3) = 5 * 1/t^3= 5/t^3
d To simplify the given expression we will use the Properties of Exponents. For this exercise, we will begin by using the Quotient of Powers Property inside the parentheses.
Now we can distribute the exponent to both factors inside parentheses. Then we will try to eliminate the exponent by splitting the terms into perfect cube factors. Let's do it!
