Simplify each expression (if it is already simplified, state that it is already simplified):

Question

a). 4x⁸-y³+33/14z

b). 4C-5C+6C-7C+8C²

c). (4D)(-5D)(6D)(-7D)(8D²)

d). -12(444cd⁵e⁶⁵⁴³/F-G)⁰-10x⁰

e). (3xy²)¹⁰(x³y)²+(2x²)⁸(-7y⁶)⁴

Answer 1

Hello Yuliya!

If I'm explaining things you already know, feel free to skip down to the bottom.

GEMDAS stands for

Grouping symbols - (parentheses)[square brackets]{and curly brackets} are "grouping symbols," and you should always simplify what's inside them before you do anything else.You need to do the ones furthest inside first.

Exponents - if one or more terms are raised to an exponent, you evaluate those second (after grouping symbols). More on that later.

Multiplication and

Division - when multiplying terms involving parentheses, such as (4x + 2)(3x + 3), you have to make sure every term in the first set of parentheses becomes multiplied by every term in the second set. There's another acronym for that, FOIL. It stands for First, Outside, Inside, Last. You multiply the First term inside each set together, then the Outside terms of each set, then the Inside terms, then the Last terms!

When multiplying or dividing two of the same variable, the exponents will add to one another. x² * x³ = x⁵.

Addition and

Subtraction - this is generally fairly easy, I think of it as "counting how many like terms there are." Like terms should be written next to one another, then added and subtracted until there's only one term. When adding or subtracting two of the same variable, the coefficients will add to one another. 2x + 3x = 5x.

Now some answers!

... Just kidding. Now some hints and deeper explanations that can lead you to the answers. I'll put the real answers right at the end.

a). 4x⁸-y³+33/14z

All the like terms are already combined, this one is good to go.

b). 4C-5C+6C-7C+8C²

You can combine all the terms with a single C by adding or subtracting their coefficients. The term with C² cannot be simplified further, because there are no other terms with C² that could be added to it.

c). (4D)(-5D)(6D)(-7D)(8D²)

All these terms can be multiplied together. Check carefully to make sure D is to the correct power at the end.

d). -12(444cd⁵e⁶⁵⁴³/F-G)⁰-10x⁰

When a variable or number is raised to the power 0, it is equal to 1.

I'm not sure what happened to the formatting of those exponents in the middle, I think they may have not pasted correctly.

e). (3xy²)¹⁰(x³y)²+(2x²)⁸(-7y⁶)⁴

When an expression in parentheses is raised to an exponent, every term in the expression is raised to that power. Furthermore, every variable and coefficient is raised to that power, even if they're part of the same term.(xy)² becomes x²y².

And finally, the real answers.

a). 4x⁸-y³+33/14z

This is already fully simplified!

b). 4C-5C+6C-7C+8C² = -2C+8C²

c). (4D)(-5D)(6D)(-7D)(8D²) = 6,720D⁶

d). -12(444cd⁵e⁶⁵⁴³/F-G)⁰-10x⁰

I think the formatting copied incorrectly. I don't want to give you a wrong answer. If you're able to show me a picture of what it originally looked like I'd be glad to help.

e). (3xy²)¹⁰(x³y)²+(2x²)⁸(-7y⁶)⁴

Distribute all the exponents across parentheses:

= (3¹⁰x¹⁰y²⁰)(x⁶y²) + (2⁸x¹⁶)(-7⁴y²⁴)

Group x's, y's, and constants:

= (3¹⁰ * x¹⁰*x⁶ * y²⁰*y²) + (2⁸*-7⁴ * x¹⁶ * y²⁴)

Take constants out of exponent form, combine like variables:

= (59,049 * x¹⁶ * y²²) + (256*2401 * x¹⁶ * y²⁴)

Multiply 256*2401 and rewrite the whole thing a little nicer:

= 59,049x¹⁶y²² + 614,656x¹⁶y²⁴

Please tell me if this helped you!