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Teachers & SchoolsAlgebra and Functions Drill 3 Problem 4. Simplify the expression.

Algebra and Functions | Simplifying expressions |

Basic Operations | Order of Operations (PEMDAS) |

CAHSEE Math | Algebra and Functions |

Language | English Language |

Please Excuse My Dear Aunt Sally...

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

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

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

its exponent value in half...

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

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

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

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

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

This means that we multiply 3 and 2 in the

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

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

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

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

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

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

We can subtract 9 and 8 to get 1,

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

Which is answer C.

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

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