All SAT Math Resources
Example Questions
Example Question #61 : Exponential Operations
Simplify:
When multiplying exponents, we just add the exponents while keeping the base the same.
Example Question #62 : Exponential Operations
Simplify:
When multiplying exponents with different bases but the same exponent, you multiply the bases and keep the exponents the same.
Example Question #63 : Exponents
Define an operation on the set of real numbers as follows:
For all real ,
Evaluate
The value of is an undefined quantity.
Set and in the expression in the definition, then simplify the exponent:
Any nonzero number raised to the power of 0 is equal to 1, so
.
Example Question #63 : Exponential Operations
Define an operation on the set of real numbers as follows:
For all real ,
Evaluate:
Set and in the expression in the definition:
The exponent simplifies as follows:
, so
Example Question #62 : Exponents
Convert the product of to base .
Although they have different bases, we know that .
Therefore
.
Remember to apply the power rule of exponents.
Finally,
.
Example Question #61 : How To Multiply Exponents
Solve for :
Now the left side equals and the right side equals 8. Hence:
Therefore must be equal to 11.
Example Question #63 : Exponents
Define an operation on the set of real numbers as follows:
For all real ,
Evaluate: .
The value of is undefined.
Set and in the expression in the definition, then simplify:
By definition,
;
setting ,
.
Substituting and ,
Also, raising a number to the power of is equivalent to taking the th root of the number; specifically, raising a number to the power of is equivalent to taking its square root. Therefore,
.
Example Question #472 : Algebra
Express in terms of .
By definition,
and
.
By the Power of a Power Rule,
,
so, by substituting,
.
Example Question #64 : Exponential Operations
Simplify the expression.
When multiplying with exponents, you must add the exponents.
Therefore, multiply the coefficients on the x terms and add the exponents
Example Question #61 : Exponents
Which of the following is equivalent to
and can be multiplied together to give you which is the first part of our answer. When you multiply exponents with the same base (in this case, ), you add the exponents. In this case, should give us because . The answer is