Which expression is equivalent to (4^0)^-3/4^-3
A. 0
B. 16
C. 64
D. 1
Given expression: (4^0)^-3 / 4^-3
We know that any number (except zero) raised to the power of 0 is equal to 1. Therefore, 4^0 = 1.
So, the expression becomes: (1)^-3 / 4^-3
Since a negative exponent represents the reciprocal of the base raised to the positive exponent, we can rewrite the expression as: 1 / 4^3
4^3 = 4 * 4 * 4 = 64
Therefore, the expression simplifies to: 1 / 64
The correct option is C. 64.
Which expression is equivalent to 4^-6/(4^-3)^2
A. 4^-1
B. 4^2
C. 0
D. 1
Given expression: 4^-6 / (4^-3)^2
We can simplify the expression by using the rule of exponents that states: (a^m)^n = a^(m * n)
Therefore, (4^-3)^2 = 4^(-3 * 2) = 4^-6
So, the expression becomes: 4^-6 / 4^-6
In any division where the base is the same, the exponents can be subtracted. So, 4^-6 / 4^-6 = 4^(-6 - (-6)) = 4^0
Any number (except zero) raised to the power of 0 is equal to 1. Therefore, 4^0 = 1.
Therefore, the expression simplifies to: 1
The correct option is D. 1.
Which expression is equivalent to 6^2/(6^-2)^4
A. 6^11
B. 6^10
C. 6^6
D. 1/6^6
Given expression: 6^2 / (6^-2)^4
We can simplify the expression by using the rule of exponents that states: (a^m)^n = a^(m * n)
Therefore, (6^-2)^4 = 6^(-2 * 4) = 6^-8
So, the expression becomes: 6^2 / 6^-8
In any division where the base is the same, the exponents can be subtracted. So, 6^2 / 6^-8 = 6^(2 - (-8)) = 6^10
Therefore, the expression simplifies to: 6^10
The correct option is B. 6^10.
Which expression is equivalent to 6^0/6^4 •6^6
A. 1/6^10
B. 1/36^24
C. 1/6^24
D. 1/36^10
Given expression: 6^0 / 6^4 • 6^6
We can simplify the expression by using the rule of exponents that states: a^m • a^n = a^(m + n)
Therefore, 6^0 / 6^4 • 6^6 = 6^(0 + 6 - 4)
Simplifying further, 6^(6 - 4) = 6^2 = 36
Therefore, the expression simplifies to: 36
The correct option is not provided in the given choices.
You sure?
Apologies for the oversight in my previous response. We will re-evaluate the expression.
Given expression: 6^0 / 6^4 • 6^6
When we divide two exponents with the same base, we subtract the exponents: a^m / a^n = a^(m - n).
So, 6^0 / 6^4 = 6^(0 - 4) = 6^(-4)
When we multiply exponents with the same base, we add the exponents: a^m • a^n = a^(m + n).
So, 6^(-4) • 6^6 = 6^(-4 + 6) = 6^2 = 36.
Therefore, the expression simplifies to 36.
The correct option is not provided in the given choices.