Simplify the expression.

(-4)^-6(-4)^-7

My answer: -4

Simplify and give the answer in scientific notation.

(5 X 10^6((3 X 10^5)

My answer: 1.5 X 10^12

(3 X 10^6)(8 X 10^-4)

My answer: 2.4 X 10^3

Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5.88 x 1012 miles. Suppose a star is 1.23 x 102 light-years from Earth. In scientific notation, approximately how many miles is it?

12.3 x 10^12
7.23 x 10^13
7.23 x 10^14
5.88 x 10^12

C

bruhhhh anyone have the answers

(-4)^-6 * (-4)^-7 = (-4)^-13

(-4)^-6 / (-4)^-7 = -4

The others look good (except for the typos)

These are my choices for the first one:

4^13
-4
13
1

so pick -4

connexus right? I needed help on this one too.

it’s -4. any negative number as a base, it doesn’t matter what exponent, is equal to 1. same with a base that has a negative number as an exponent. basically you cant use negatives so they automatically convert to 1.

To simplify the expression (-4)^-6(-4)^-7, we need to first use the rule of exponents which states that when you raise a negative number to an even power, the result is always positive. Therefore, (-4)^-6 will become 4^6.

Next, we multiply 4^6 by (-4)^-7. To simplify this, we again use the rule of exponents. When you raise a negative number to an odd power, the result remains negative. Therefore, (-4)^-7 will stay as (-4)^-7.

Now, we can multiply the two expressions together: 4^6 * (-4)^-7.

To simplify this multiplication, we need to convert the bases to the same value. Since 4 can be expressed as (-4)^2, we can rewrite the expression as (-4)^2^6 * (-4)^-7.

Using the rule of exponents which states that when you raise a power to another power, you multiply the exponents, we have (-4)^(2*6) * (-4)^-7.

Simplifying further, we have (-4)^12 * (-4)^-7.

Again, we can combine the expressions by adding the exponents: (-4)^(12-7), which gives us (-4)^5.

Finally, we raise -4 to the 5th power, which evaluates to -1024.

Hence, the simplified expression is -1024.

Therefore, your answer of -4 is incorrect.

Moving on to the next question, we need to simplify the expression (5 x 10^6) * (3 x 10^5) and give the answer in scientific notation.

To multiply the numbers, we simply multiply the coefficients (5 * 3) and add the exponents of the same base (10^6 * 10^5).

The result is 15 x 10^(6+5) which simplifies to 15 x 10^11.

Therefore, the expression (5 x 10^6) * (3 x 10^5) simplifies to 15 x 10^11 in scientific notation.

Moving on to the next question, we need to simplify the expression (3 x 10^6) * (8 x 10^-4) and give the answer in scientific notation.

Again, to multiply the numbers, we multiply the coefficients (3 * 8) and add the exponents of the same base (10^6 * 10^-4).

The result is 24 x 10^(6-4) which simplifies to 24 x 10^2.

Therefore, the expression (3 x 10^6) * (8 x 10^-4) simplifies to 24 x 10^2 in scientific notation.

Moving on to the last question, we need to approximate how many miles a star is when it is 1.23 x 10^2 light-years away from Earth. We know that one light-year is approximately 5.88 x 10^12 miles.

To find the answer in miles, we multiply the number of light-years (1.23 x 10^2) by the number of miles in one light-year (5.88 x 10^12).

Multiplying the coefficients (1.23 * 5.88) gives us approximately 7.2232.

Now, we add the exponents of 10. Since we are multiplying two numbers in scientific notation, we add the exponents: 10^2 + 10^12.

The result is 10^(2+12) which simplifies to 10^14.

Therefore, the star is approximately 7.2232 x 10^14 miles away from Earth.

Hence, the correct answer is 7.23 x 10^14 (rounded to two decimal places).