8.A number raised to a negative exponent is negative.

Always, never , or sometimes.

7. Evaluate 1/2a^-4b^2 a = -2 and b = 4.

6. Simplify. Write in scientific notation. (9 x 10^-3)^2

Thanks to anyone who helps right away and need right answer from the people who have already taken this test.

8.

4^-3 = 1/4^3 = 1/64
(-2)^-3 = 1/(-2)^3 = 1/-8

7 , the way you typed it ...

(1/2)a^-4 b^2
= (1/2)(1/(-2)^4 (4)^2
= (1/2)(1/16)(16) = 1/2

6. (9 x 10^-3)^2 = 1.8 x 10^-6

8. Sometimes.

When a number is raised to a negative exponent, the result depends on whether the base is positive or negative. If the base is positive, the result will be a positive number. For example, 2^-3 = 1/(2^3) = 1/8 = 0.125, which is positive. However, if the base is negative, the result will be a negative number. For example, (-2)^-3 = 1/((-2)^3) = 1/(-8) = -0.125, which is negative.

7. To evaluate the expression 1/2a^-4b^2 when a = -2 and b = 4, substitute the given values of a and b into the expression:

1/2(-2)^-4(4)^2 = 1/2(1/(-2)^4)(16)
= 1/2(1/16)(16)
= (1/2)(1)
= 1/2

So, when a is -2 and b is 4, the value of the expression is 1/2.

6. To simplify (9 x 10^-3)^2 and write it in scientific notation, we need to multiply the base by itself and multiply the exponents:

(9 x 10^-3)^2 = 9^2 x (10^-3)^2
= 81 x 10^(-3 x 2)
= 81 x 10^-6

The final answer in scientific notation is 8.1 x 10^-5.