Applying the laws of exponents

In summary, the conversation is about simplifying algebraic expressions with exponents. The first problem involves simplifying a power of a product, while the second problem involves simplifying fractions with negative exponents. The final response confirms that both answers are correct.
  • #1
drop
14
0
Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

7) Simplify (5x^3yz^2)^2(-3x^3y^4z)

My answer: -75x^9y^6z^5

8) Simplify the problem below using positive exponents only.

8a^-2b^3c^4
18a^5b^-3c

My Answer:
4b^6c^3
9a^7
 
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  • #2
Re: Please check my answers - 4

drop said:
Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

7) Simplify (5x^3yz^2)^2(-3x^3y^4z)

My answer: -75x^9y^6z^5

8) Simplify the problem below using positive exponents only.

8a^-2b^3c^4
18a^5b^-3c

My Answer:
4b^6c^3
9a^7

Both correct.

I underlined your numerators there. :)
 

FAQ: Applying the laws of exponents

What are the basic laws of exponents?

The basic laws of exponents are the product rule, quotient rule, power rule, zero exponent rule, and negative exponent rule.

How do you apply the product rule in exponents?

The product rule states that when multiplying two terms with the same base, you add the exponents. For example, x^3 * x^2 = x^(3+2) = x^5.

What is the quotient rule in exponents?

The quotient rule states that when dividing two terms with the same base, you subtract the exponents. For example, x^5 / x^2 = x^(5-2) = x^3.

How do you simplify expressions with negative exponents?

To simplify expressions with negative exponents, you can move the term with the negative exponent to the denominator and change the sign of the exponent to positive. For example, x^-3 = 1/x^3.

Can the laws of exponents be applied to any base?

Yes, the laws of exponents can be applied to any base, as long as the base is the same for all terms being multiplied or divided.

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