All GED Math Resources
Example Questions
Example Question #1 : Exponents
Solve:
Example Question #2 : Exponents
Write the following expression in expanded form:
An exponent indicates the amount of times a number (or variable) should be multiplied by itself. For example, .
In this instance, .
Example Question #2 : Exponents
Simplify:
Example Question #4 : Exponents
Express 45,000,000 in scientific notation.
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 #1 : Exponents
Express 0.000000038 in scientific notation.
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 #3 : Exponents
Which of the following is not equal to ?
Do not use a calculator.
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 #3 : Exponents
Without using a calculator, evaluate .
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 #4 : Exponents
Evaluate without using a calculator:
Example Question #5 : Exponents
Simplify the expression:
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 #3 : Exponents
Without using a calculator, evaluate:
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. Apply this power, along with the power of a quotient property: