Question

Which expression is equivalent to (3^-4)^6
A. 3^24
B. 3^2
C. 3^10
D. 1/3^24
Answer
Which expression is equivalent to 3/3^2?
A. 3
B. 1/9
C. 1/3
D. 1/27
Answer
Which expression is equivalent to (5^6)^-5?
A. 1/5^35
B. 5
C. 1/5^11
D. 1/5^30
Answer
Which expression is equivalent to 2^-1/2^4
A. 1/32
B. 8
C. 1/16
D. 1/8
Answer
Which expression is equivalent to 3^0 • 3^-3?
A. 1
B. 0
C. 1/3^3
D. 3^3
Answer
Which expression is equivalent to (5^-1)^2?
A. 1/25
B. 5
C. 125
D. 1/125
Answered by GPT 3.5
To find the equivalent expression, you need to simplify (3^-4)^6.

First, let's simplify the exponent. When you raise a power to another power, you multiply the exponents. Therefore, (-4)(6) = -24.

Now, we have (3^-24). The negative exponent indicates that it is the reciprocal of 3^24. So, (3^-24) = 1/(3^24).

Therefore, the expression (3^-4)^6 is equivalent to option D: 1/3^24.
Answered by GPT 3.5
To find the equivalent expression, you need to simplify 3/3^2.

First, let's simplify the exponent. 3^2 = 3 * 3 = 9.

Now, we have 3/9. To simplify this further, notice that both 3 and 9 are divisible by 3.

3 divided by 3 is 1, and 9 divided by 3 is 3. Therefore, 3/9 simplifies to 1/3.

Therefore, the expression 3/3^2 is equivalent to option C: 1/3.
Answered by GPT 3.5
To find the equivalent expression, you need to simplify (5^6)^-5.

To simplify this expression, you need to multiply the exponents. So, (-5)(6) = -30.

Now, we have (5^-30). The negative exponent indicates that it is the reciprocal of 5^30. So, (5^-30) = 1/(5^30).

Therefore, the expression (5^6)^-5 is equivalent to option D: 1/5^30.
Answered by GPT 3.5
To find the equivalent expression, you need to simplify 2^-1/2^4.

First, let's simplify the exponents. 2^4 = 2 * 2 * 2 * 2 = 16.

Now, we have 2^-1/16.

Recall that a negative exponent indicates that it is the reciprocal of the positive exponent. So, 2^-1 = 1/2^1.

Substituting these values back into the expression, we have (1/2^1)/16.

Simplifying the numerator, we have 1/2 divided by 16.

To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, (1/2) * (1/16) = 1/32.

Therefore, the expression 2^-1/2^4 is equivalent to option A: 1/32.
Answered by GPT 3.5
To find the equivalent expression, you need to simplify 3^0 • 3^-3.

Recall that any number raised to the power of 0 is equal to 1. So, 3^0 = 1.

Next, to simplify 3^-3, remember that a negative exponent indicates the reciprocal of the positive exponent. Therefore, 3^-3 = 1/3^3.

Now, substitute these simplified values back into the expression: 1 • 1/3^3.

To multiply fractions, multiply the numerators and multiply the denominators. 1 • 1/3^3 = 1/27.

Therefore, the expression 3^0 • 3^-3 is equivalent to option C: 1/3^3.
Answered by GPT 3.5
To find the equivalent expression, you need to simplify (5^-1)^2.

To simplify this expression, you need to multiply the exponents. So, (-1)(2) = -2.

Now, we have (5^-2). The negative exponent indicates that it is the reciprocal of 5^2. So, (5^-2) = 1/(5^2).

Remember that 5^2 is equal to 5 * 5 = 25.

Therefore, the expression (5^-1)^2 is equivalent to option A: 1/25.