All SAT Math Resources
Example Questions
Example Question #41 : Exponents
Simplify into base .
Can't be simplified.
We need to get them to bases of . All of those bases derive from bases of but raised to different powers. is the same as as anything raised to the first power is the same as its base. .
Next, . Since it's raised to the fourth power, let's make a proportion.
.
The top represents the power of base . The bottom represents the power of base . When we cross-multiply, we have . So .
Finally, is the same as . Let's do another proportion.
.
The top represents the power of base . The bottom represents the power of base .Wen we cross-mulltiply, we get . So .
With the same bases, we can add the exponents.
We have .
Example Question #41 : Exponents
can be stated as which of the following?
2 and 3
1 only
2 only
3 only
1 and 3
2 and 3
This will test your knowledge of a specific exponential property: . Knowing that, 2 and 3 do come out to , while 1 comes out to only .
Example Question #43 : How To Multiply Exponents
Simplify:
1
When an exponent is raised to the power of another exponent, we multiply the exponents together.
For our x-value, the exponent will be
For our y-value, the exponent will be
Therefore,
Example Question #452 : Algebra
Solve for in terms of :
Example Question #42 : Exponents
Evaluate
When multiplying exponents of the same base, we just add the exponents and keep the base the same.
Example Question #43 : Exponents
Evaluate
When multiplying exponents of the same base, we just add the exponents and keep the base the same.
Example Question #44 : Exponents
Evaluate
Although we have different bases, we know that Therefore we have .
Example Question #41 : How To Multiply Exponents
Simplify
Simplify the numerator
Pull an x out of each term in the numerator
The x in the numerator and the x in the denominator cancel
Example Question #46 : Exponents
Solve:
When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 6+12, to get a new exponent of 18:
Example Question #47 : Exponents
Solve:
When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3: