Exponents and Powers on Your Exam
You will see several problems involving exponents and powers on your standardized exam.
To see the free sample problems on exponents, please go to the next section.
Exponents and Powers – Exercises
Instructions: Solve the exercises on exponents and powers below. The answers are given in the next section. You may wish to view the examples on the rules for exponents and powers in the next section first.
1) a3 × a4 = ?
2) (y2)4 = ?
3) (3x2)(6x6) = ?
4) \(\frac {3^8}{3^5} = ?\)
5) Express as a fraction:
6) Express as a radical:
7) a × b0 = ?
8) x2 × x3 × x5= ?
9) [(x2)4]3 = ?
10) (5ab5)(–6ab3) = ?
Exponents and Powers – Answers
1) The correct answer is: a7
a3 × a4 = a3 + 4 = a7
2) The correct answer is: y8
(y2)4 = y2 x 4 = y8
3) The correct answer is: 18x8
(3x2)(6x6) = (3 × 6)(x2 + 6)= 18x8
4) The correct answer is: 27
\(\frac {3^8}{3^5} =\)
38 ÷ 35 =
38 – 5 =
33 =
3 × 3 × 3 = 27
5) The correct answer is as follows:
6) The correct answer is as follows:
7) The correct answer is: a
a × b0 = a × 1 = a
8) The correct answer is: x10
x2 × x3 × x5 = x2 + 3 + 5 = x10
9) The correct answer is: x24
[(x2)4]3 = x2 x 4 x 3 = x24
10) The correct answer is: -30a2b8
(5ab5)(–6ab3) = (5 × -6)(a × a)(b5 + 3) = -30a2b8
Exponents – Definitions
An exponent shows how many times a number is to be multiplied times itself.
The number or variable is called the base.
A number or variable with an exponent is raised to the power of the exponent.
So, a4 is expressed verbally as “a to the power of 4.”
Exponents and Powers – Rules
Same base numbers with different exponents
52 × 57 = ?
The base number for the equation above is 5.
If your base number is the same, you add the exponents when you multiply.
52 × 57 = 5(2 + 7) = 59 = 1,953,125
Remember: Don’t confuse multiplication with addition. The result is completely different.
52 + 57 = 25 + 78, 125 = 78,150
Base numbers with a common variable
(2x2)(–4x4) = ?
If the base numbers have a common variable and you need to multiply them, multiply the numbers in front of the variable, and add the exponents.
(2x2)(–4x4) = –8x6
Exponent raised to a power
When you have an exponent raised to a power, you can multiply the exponents.
(x3)2 = x6
Fraction as exponent
You may see numbers that have fractions in the exponent.
Put the base number inside the radical sign.
The denominator of the fraction in the exponent becomes the root of the radical.
The numerator of the fraction in the exponent is the new exponent.
Fractions that have exponents
\(\frac {x^9}{x^5} = ?\)
On your exam, there may be questions that have factions with exponents in both their numerator and denominator.
Perform division and subtract the exponents when the base number is the same.
\(\frac {x^9}{x^5} =\)
x9 ÷ x5 = x9 – 5 = x4
Negative exponents
When you see a negative exponent, you remove the negative sign on the exponent by expressing the number as a fraction, with 1 as the numerator.
Zero exponent
When the base is not equal to zero, any number or variable to the power of zero is equal to 1.
a0 = 1
Now try to memorize the exponent rules above.
Exponent Calculator
If you have any questions on exponents that have not been answered in this post, you can try using the exponent calculator.
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