CAHSEE Math 3.4 Algebra and Functions

Algebra and Functions Drill 3 Problem 4. Simplify the expression.

Algebra and FunctionsSimplifying expressions
Basic OperationsOrder of Operations (PEMDAS)
CAHSEE MathAlgebra and Functions
LanguageEnglish Language

Transcript

00:27

Please Excuse My Dear Aunt Sally...

00:29

or parentheses, exponents, multiplication/division, and addition/subtraction.

00:35

PEMDAS tells us to work with the variables inside the parentheses first.

00:40

n-cubed looks good... but the square root of n to the 6th gives us the effect of dividing

00:46

its exponent value in half...

00:48

...so the square root of n to the 6th can be simplified as n cubed.

00:52

We can move to exponents next. Looking at our first quantity, we have the

00:56

quantity n cubed... squared. One of the properties of exponents tells us

01:01

that, for any number, a, with exponents m and n, a to the power of m,

01:07

to the power of n, equals a to the power of m times n.

01:16

This means that we multiply 3 and 2 in the

01:18

expression n cubed squared, to get n to the 6th.

01:24

Utilizing more properties of exponents... ...specifically, the one which states that

01:28

a to the m times a to the n equals a to the m plus n... 

01:35

and the one which states that a to the m over a to the n equals a to the m minus n...

01:43

...we can add 6 plus 3 equals 9 to get n to the 9th in the numerator.

01:47

The expression then becomes n to the 9th over n to the 8th.

01:51

We can subtract 9 and 8 to get 1,

01:54

so we're left with n to the first power, or just... n.

01:57

Which is answer C.

01:59

You'll need 'em again, so make sure you commit those properties of exponents to memory.

02:03

Trust us... they're some of the most valuable properties on the board.