1) Write the expression as a fraction with a positive exponent. Do not evaluate the expression.

307 to the power of -712

11 answers

1/(307^712)
1) For an eighth grader, Write the expression as a fraction with a positive exponent. Do not evaluate the expression.
307 to the power of -712
To write the expression 307 to the power of -712 as a fraction with a positive exponent, we can rewrite it as 1 over 307 to the power of 712.

So, the expression as a fraction with a positive exponent is: 1/(307^712)
What is 1 to the power of 0?
Any number (except 0) raised to the power of 0 is equal to 1. So, 1 to the power of 0 is equal to 1.
What is (12^3)^1
(12^3)^1 is equal to 12^3, which equals 12 * 12 * 12 = 1,728.
Which expression is equivalent to 12^-3/ 2^-3 ?

A. 6^3/6^-1
B. 1/6^3
C. 6^0
D. (6^-2)^-1
To determine which expression is equivalent to 12^-3 / 2^-3, we can simplify the expression first.

12^-3 = 1/12^3 = 1/1728
2^-3 = 1/2^3 = 1/8

So, 12^-3 / 2^-3 = (1/1728) / (1/8) = (1/1728) * (8/1) = 8/1728 = 1/216

Now, let's examine the answer choices:

A. 6^3 / 6^-1 = 216 / 6 = 36,
B. 1 / 6^3 = 1 / 216,
C. 6^0 = 1,
D. (6^-2)^-1 = (1/6^2)^-1 = (1/36)^-1 = 36.

Among the answer choices, B (1/6^3) is equivalent to 12^-3 / 2^-3.
1) Simplify. Express your answer using positive exponents.

(3fgh)(4fgh^5)
To simplify the expression (3fgh)(4fgh^5), we multiply the coefficients and multiply the variables with the same base:

3 * 4 = 12
f * f = f^2
g * g = g^2
h * h^5 = h^(1+5) = h^6

Therefore, the simplified expression is:
12f^2g^2h^6
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