Math Problem Statement

Simplify the expression y^7 · y^(-10)

Solution

To simplify the expression y7y10y^7 \cdot y^{-10}, we use the property of exponents that states:

aman=am+na^m \cdot a^n = a^{m+n}

In this case: y7y10=y7+(10)=y3y^7 \cdot y^{-10} = y^{7 + (-10)} = y^{-3}

Since y3y^{-3} is equivalent to 1y3\frac{1}{y^3}, the correct answer is:

1y3\frac{1}{y^3}

So, the correct option is: 1y3\frac{1}{y^3}.

Would you like further explanation or have any questions?

Here are 5 related questions that could help expand your understanding:

  1. How do you simplify expressions with different bases and exponents?
  2. What happens when you multiply two expressions with the same base but with negative exponents?
  3. How would you simplify (y4y2)y3(y^4 \cdot y^{-2}) \cdot y^3?
  4. How can you rewrite a negative exponent as a positive exponent in the denominator?
  5. What is the rule for dividing powers with the same base?

Tip: When multiplying exponents with the same base, simply add the exponents.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Exponent Rules

Formulas

a^m · a^n = a^(m+n)
a^(-n) = 1/a^n

Theorems

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Suitable Grade Level

Grades 7-9