Simplify expression with laws of indices

In summary, the user was struggling with a math problem involving negative powers and was unsure how to proceed. Another user provided a strategy to get rid of the negative powers by using the rule a^-1 = 1/a. The final solution involved simplifying the expression and resulted in y^35 * z^20 / x^26. The user thanked the helper for their assistance.
  • #1
dmarley
2
0
Helping my daughter with her math and hit this one and not sure how to advise. All help welcome(x-2y10)3 / (x-4yz4)-5

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
 
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  • #2
dmarley said:
(x-2y10)3 / (x-4yz4)-5
This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
z^(4*(-5)) = z^(-20)
Now move to numerator:
z^(-20) = z^20

So you'll end up with: y^35 * z^20 / x^26
 
  • #3
dmarley said:
Helping my daughter with her math and hit this one and not sure how to advise. All help welcome(x-2y10)3 / (x-4yz4)-5

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
The basic rule is \(\displaystyle a^{-1} = \dfrac{1}{a}\) and \(\displaystyle \left ( a^{-1} \right ) ^{-1} = a\).

Strategy: Get rid of those pesky negative powers.
\(\displaystyle \dfrac{ \left ( x^{-2}y^{10} \right ) ^3 }{ \left ( x^{-4} y z^4 \right ) ^{-5} }\)

\(\displaystyle = \left ( x^{-2}y^{10} \right ) ^3 \left ( x^{-4} y z^4 \right ) ^5\)

\(\displaystyle = \left ( \dfrac{y^{10}}{x^2} \right ) ^3 \left ( \dfrac{yz^4}{x^4} \right ) ^5\)

Can you finish?

-Dan
 
  • #4
topsquark - thanks for the help

following your basic rule really helped out and clarified for us.
 

FAQ: Simplify expression with laws of indices

What are the basic laws of indices?

The basic laws of indices are the power of a power rule, the power of a product rule, the power of a quotient rule, the product of powers rule, and the quotient of powers rule. These laws help simplify expressions with exponents.

How do I simplify an expression with indices?

To simplify an expression with indices, you can use the laws of indices to rewrite the expression in a simpler form. This involves combining like terms, cancelling out common factors, and applying the appropriate index laws.

Can I use the laws of indices with negative and fractional exponents?

Yes, the laws of indices can also be applied to expressions with negative and fractional exponents. For example, the power of a power rule can be used to simplify expressions with negative exponents, while the power of a quotient rule can be used for expressions with fractional exponents.

What is the difference between the power of a power rule and the product of powers rule?

The power of a power rule states that when raising a power to another power, you can multiply the exponents. On the other hand, the product of powers rule states that when multiplying two powers with the same base, you can add the exponents. These rules are similar but have different applications in simplifying expressions with indices.

Can I use the laws of indices to solve equations with exponents?

Yes, the laws of indices can also be used to solve equations with exponents. By simplifying both sides of the equation using the appropriate index laws, you can isolate the variable and solve for its value.

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