PSAT Math : Exponents

Example Questions

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Simplify:

Explanation:

Now

Example Question #261 : Exponents

Solve for .

Explanation:

If we combine into a single logarithmic function we get:

Solving for  we get .

Example Question #261 : Exponents

If  is the complex number such that , evaluate the following expression:

Explanation:

The powers of i form a sequence that repeats every four terms.

i= i

i2 = -1

i3 = -i

i4 = 1

i5 = i

Thus:

i25 = i

i23 = -i

i21 = i

i19= -i

Now we can evalulate the expression.

i25 - i23 + i21 - i19 + i17..... + i

= i + (-1)(-i) + i + (-1)(i) ..... + i

= i + i + i + i + ..... + i

Each term reduces to +i. Since there are 13 terms in the expression, the final result is 13i.

Example Question #1241 : Psat Mathematics

Express 0.000000076 in scientific notation.

Explanation:

Write the number:

Counting the number of places, move the decimal point to the right until it is after the first nonzero digit:

The resulting number is 7.6; the number of places the decimal point moved to the right was 8. In scientific notation, this number is .

Example Question #581 : Algebra

Express the square of  in scientific notation.

Explanation:

Take advantage of the exponent rules.

Example Question #141 : Exponents

The number  is equivalent to which of the following?

Explanation:

Each of the answers to this question are in scientific notation. To determine the exponent on the 10, see how many places you need to move the decimal over to get from your original number to 2.79.

Because the decimal place moves 5 places, the exponent will be 5, and because the decimal moves to the RIGHT, the exponent is going to be negative.

So the answer to the quesiton is

Example Question #4 : How To Use Scientific Notation

Put the following value in scientific notation: