GED Math : Exponents

Example Questions

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Solve:

Explanation:

Example Question #462 : Numbers And Operations

Write the following expression in expanded form:

Explanation:

An exponent indicates the amount of times a number (or variable) should be multiplied by itself. For example, .

In this instance, .

Simplify:

Explanation:

Example Question #1 : Exponents

Express 45,000,000 in scientific notation.

Explanation:

Write the number with a decimal point and without commas:

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

The resulting  number is 4.5; the number of places the decimal point moved to the left was 7. In scientific notation, this number is .

Example Question #5 : Exponents

Express 0.000000038 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 3.8; the number of places the decimal point moved to the right was 8. In scientific notation, this number is .

Example Question #2 : Exponents

Which of the following is not equal to  ?

Do not use a calculator.

Explanation:

A positive number raised to any real power is positive.  and  are the opposites of powers of positive numbers; they are therefore the opposites of positive numbers, making both negative.

A negative number raised to an odd power, such as , is negative.

A negative number raised to an even power, such as , is positive.

is the only positive number among the choices and can be deduced as the correct choice.

Example Question #7 : Exponents

Without using a calculator, evaluate .

Explanation:

For any nonzero  and for any . Equivalently, any number raised to a negative power is equal to the reciprocal of that number raised to the power of the absolute value of the exponent.

The reciprocal of a number is the quotient of 1 and the number, so the reciprocal of 0.4 is

.

Therefore,

, which is the correct response.

Example Question #8 : Exponents

Evaluate without using a calculator:

Explanation:

Example Question #9 : Exponents

Simplify the expression:

Explanation:

A number or variable can be raised to a negative power by taking the reciprocal of the same number raised to the power of the absolute value of the exponent.

Example Question #1 : Exponents

Without using a calculator, evaluate: