help me I have a high school entrance exam soon, what should I study to get a good score?

Thank you guys, all of these answers are helping me

Is this correct? Product: if you multiply a number with an exponent by the same number but with a different exponent, you add the two exponents together, leaving the whole number as is. Power: If you multiply a number with an exponent by an exponent, you multiply the two exponents and leave the base number alone. Quotient: Since division is the opposite of multiplication, naturally the addition power of multiplying exponents becomes subtraction when you divide them. (Be careful with negative numbers! They have tripped me up several times.) Zero exponent rule: strange and tricky. imagine it like this: you have a number you want to multiply exponentially, say, 7. Instead of thinking this as the base, think of the neutral base as 1. If 1 is multiplied exponentially by 7 zero times, it wasn't multiplied at all. so it remains its original self: 1. If it was multiplied once, it would be 7. (This is just an idea of how to think about it! please someone comment if you see a flaw in my logic.) Your friendly neighborhood Spider-girl

All that is correct! I like how you describe each one in your own words. It shows a true understanding of the concept!

Main content

Course: Algebra 1 > Unit 11

Lesson 3: Simplifying square roots

Exponents & radicals: FAQ

Google Classroom

Frequently asked questions about exponents & radicals

What are exponent properties?

We can use these properties of exponents to help us simplify expressions involving exponents:

Product rule:

x^{a} \times x^{b} = x^{a + b}

. For example,

x^{2} \times x^{3} = x^{5}

Power rule:

(x^{a})^{b} = x^{a b}

. For example,

(x^{2})^{3} = x^{6}

Quotient rule:

\frac{x^{a}}{x^{b}} = x^{a - b}

. For example,

\frac{x^{5}}{x^{2}} = x^{3}

Zero exponent rule:

x^{0} = 1

. For example,

7^{0} = 1

Practice with our Multiply & divide powers (integer exponents) exercise.

Practice with our Powers of products & quotients (integer exponents) exercise.

What are radicals?

A radical is a symbol that we use to write square roots, cube roots, and other roots. For example,

\sqrt{81}

is the square root of

81

, or the number we can multiply by itself to get

81

. Another example is

\sqrt[3]{8}

, which is the cube root of

8

, or the number we can multiply by itself to get

8

Practice with our Square roots exercise.

Practice with our Cube roots exercise.

What are some common ways to simplify square roots?

One common way to simplify square roots is to factor the radicand (the number inside the square root symbol) into perfect squares. For example,

\sqrt{50}

can be simplified by factoring

50

into

25

times

2

\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}

Practice with our Simplify square roots exercise.

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Evan Evan
Posted a year ago. Direct link to Evan Evan's post “There's a mistake on this...”
There's a mistake on this page where it says "the cubed root of 8 is the number we can multiply by itself to get 8". It should actually say the number we can multiply by itself 3 times to get 8 (because it's the cubed root, not the square root)
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Qyqjaari The GOAT
Posted 9 months ago. Direct link to Qyqjaari The GOAT's post “help me I have a high sch...”
help me I have a high school entrance exam soon, what should I study to get a good score?
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(7 votes)
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- Qyqjaari The GOAT
  Posted 9 months ago. Direct link to Qyqjaari The GOAT's post “Thank you guys, all of th...”
  Thank you guys, all of these answers are helping me
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  (4 votes)
Evangeline Viklund {S/H}
Posted 3 months ago. Direct link to Evangeline Viklund {S/H}'s post “Is this correct? Product...”
Is this correct?

Product: if you multiply a number with an exponent by the same number but with a different exponent, you add the two exponents together, leaving the whole number as is.

Power: If you multiply a number with an exponent by an exponent, you multiply the two exponents and leave the base number alone.

Quotient: Since division is the opposite of multiplication, naturally the addition power of multiplying exponents becomes subtraction when you divide them. (Be careful with negative numbers! They have tripped me up several times.)

Zero exponent rule: strange and tricky. imagine it like this: you have a number you want to multiply exponentially, say, 7. Instead of thinking this as the base, think of the neutral base as 1. If 1 is multiplied exponentially by 7 zero times, it wasn't multiplied at all. so it remains its original self: 1. If it was multiplied once, it would be 7. (This is just an idea of how to think about it! please someone comment if you see a flaw in my logic.)

Your friendly neighborhood Spider-girl
Button navigates to signup pageComment on Evangeline Viklund {S/H}'s post “Is this correct? Product...”
(3 votes)
Answer
- FreeRadical
  Posted 3 months ago. Direct link to FreeRadical's post “All that is correct! I li...”
  All that is correct! I like how you describe each one in your own words. It shows a true understanding of the concept!
  Comment on FreeRadical's post “All that is correct! I li...”
  (3 votes)
aylaweller
Posted 9 days ago. Direct link to aylaweller's post “can i see a video explini...”
can i see a video explining thins
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mwyatt27
Posted 7 months ago. Direct link to mwyatt27's post “What's a rational number?”
What's a rational number?
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_
Posted 3 months ago. Direct link to _'s post “Is this a chat room?”
Is this a chat room?
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Slay
Posted 4 months ago. Direct link to Slay's post “hey.... how can i tell th...”
hey.... how can i tell the different rules apart?
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clairey
Posted 9 months ago. Direct link to clairey's post “Can I find out which perf...”
Can I find out which perfect squares I use to fully simplify and replace the radicand? For example, the square root of 160 could be simplified like 2 and the square root of 40, but the fully simplified answer is 4 to the square root of 10.
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- Ron Kempke
  Posted 5 months ago. Direct link to Ron Kempke's post “The square root of 40 isn...”
  The square root of 40 isn't simplified since 40 = 4 x 10, with the 4 being a perfect square.
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Natalie
Posted a year ago. Direct link to Natalie's post “confused”
confused
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LiliaH
Posted a year ago. Direct link to LiliaH's post “Why do we do this”
Why do we do this
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- Ron Kempke
  Posted 5 months ago. Direct link to Ron Kempke's post “...because you're a stude...”
  ...because you're a student, not a mature adult.
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  (0 votes)