Hello, Bot. May I ask for your help with a few questions?
Of course! I'm here to help. What questions do you have?
(Laws of Exponents with Integer Exponents MC)
What is the value of the quantity negative one fourth cubed all raised to the power of negative 3?
a) -1
b) 1
c) -262,144
d) 262,144
To simplify the expression, let's tackle it step by step:
The quantity "-1/4 cubed" implies raising -1/4 to the power of 3, which is (-1/4)^3.
((-1/4)^3) = (-1/4) * (-1/4) * (-1/4) = -1/64.
Now, we need to raise -1/64 to the power of -3, which is ((-1/64)^(-3)).
Recall that negative exponent signifies taking the reciprocal. Thus, (-1/64)^(-3) = (1/(-1/64))^3 = (-64)^3.
Calculating (-64)^3, we find that it is equal to -262,144.
Therefore, the value of the given expression is -262,144.
So, the correct answer is c) -262,144.
(Laws of Exponents with Integer Exponents LC)
Create an equivalent expression for 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six
To create an equivalent expression, let's simplify it step by step:
First, let's simplify the expression within the parentheses: 1.4 cubed is equal to (1.4)^3, and 1.2 raised to the fourth power is equal to (1.2)^4.
So, the expression within the parentheses becomes (1.4)^3 / (1.2)^4.
Now, we need to raise this expression to the power of negative six: ((1.4)^3 / (1.2)^4)^(-6).
Recall that when we raise an expression to a negative exponent, it signifies taking the reciprocal. Thus, ((1.4)^3 / (1.2)^4)^(-6) = ((1.2)^4 / (1.4)^3)^6.
Therefore, an equivalent expression for 1.4 cubed over 1.2 raised to the fourth power, all raised to the power of negative six, is ((1.2)^4 / (1.4)^3)^6.