Gr 10 Math Ch 2: Exponent Laws

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Questions and Answers

What is the result of simplifying the expression $a^5 imes a^3$?

  • $a^{15}$
  • $a^8$ (correct)
  • $a^{5-3}$
  • $a^2$

What does the expression $\frac{a^7}{a^2}$ simplify to?

  • $a^{9}$
  • $a^5$ (correct)
  • $a^4$
  • $a^{7-2}$

Which of the following expressions is equivalent to $(xy)^3$?

  • $x^3y^3$ (correct)
  • $xy^3$
  • $x^{3y}$
  • $x^3y^2$

What is the value of $a^0$ when $a$ is any non-zero number?

<p>1 (B)</p> Signup and view all the answers

Which of these is the correct application of the negative exponent law?

<p>$a^{-3} = rac{1}{a^3}$ (A)</p> Signup and view all the answers

Which statement about simplifying $(\frac{a}{b})^2$ is true?

<p>$\frac{a^2}{b^2}$ (A)</p> Signup and view all the answers

How can the expression $a^4b^3/a^2b^1$ be simplified?

<p>$a^2b^2$ (C)</p> Signup and view all the answers

Which method is NOT typically used to simplify exponential expressions?

<p>Increasing the exponents (C)</p> Signup and view all the answers

What is the result of simplifying $(a^3b^2)^2$ using the exponent laws?

<p>a^6b^4 (B)</p> Signup and view all the answers

Which expression correctly represents the application of the negative exponent law?

<p>a^{-5} = rac{1}{a^5} (D)</p> Signup and view all the answers

When applying the law of division of exponents, what does $ rac{a^m}{a^3}$ simplify to?

<p>a^{m-3} (B)</p> Signup and view all the answers

How would you simplify the expression $a^5 imes a^{-2}$?

<p>a^{3} (A)</p> Signup and view all the answers

What is the correct result of this expression: $( rac{2}{3})^2$?

<p>$ rac{4}{9}$ (C)</p> Signup and view all the answers

Which of the following represents the factorization of $a^2 - b^2$?

<p>(a - b)(a + b) (C)</p> Signup and view all the answers

How do you simplify a complex fraction such as $ rac{a^5}{b^2} imes rac{b^3}{a^2}$?

<p>a^{3}b^{1} (B)</p> Signup and view all the answers

Which of the following statements correctly applies the zero exponent law?

<p>a^{0} = 1 (D)</p> Signup and view all the answers

What expression does the law of raising a product to a power state for two numbers a and b?

<p>(ab)^n = a^n b^n (C)</p> Signup and view all the answers

How should the expression $a^4 imes a^{-5}$ be simplified using the law of exponents?

<p>$a^{-1}$ (C)</p> Signup and view all the answers

If a and b are positive real numbers, which expression correctly represents the application of the quotient of exponents rule?

<p>$ rac{a^m}{b^n} = a^{m-n}$ (A)</p> Signup and view all the answers

Which statement correctly represents the negative exponent law?

<p>$a^{-m} = rac{1}{a^{m}}$ (D)</p> Signup and view all the answers

What is the result of applying the law of raising a power to a power to the expression $(a^2)^3$?

<p>$a^{6}$ (A)</p> Signup and view all the answers

What will be the result of simplifying the expression $ rac{(ab)^2}{a^3b^2}$?

<p>$a^{-1}$ (A)</p> Signup and view all the answers

Which of the following expressions illustrates the law of zero exponent correctly?

<p>$a^0 = 1$ for any a != 0 (D)</p> Signup and view all the answers

When simplifying the expression $a^5b^2/a^3b^1$, which method should you apply?

<p>Cancel out common factors (C)</p> Signup and view all the answers

What is the result of applying the law of raising a power to a power on the expression $(a^3)^4$?

<p>$a^{12}$ (B)</p> Signup and view all the answers

Which law of exponents allows you to simplify the expression $( rac{a^2}{b^3})^3$?

<p>Raising a Quotient to a Power (A)</p> Signup and view all the answers

When simplifying an expression like $a^5 imes a^{-3}$, which step correctly applies exponent laws?

<p>Add the exponents: $a^{2}$ (B)</p> Signup and view all the answers

In the exponent expression $a^{-2} imes a^4$, what is the final simplified form?

<p>$a^2$ (A)</p> Signup and view all the answers

Which of the following is the result of applying the zero exponent law to the expression $b^0$?

<p>$1$ (B)</p> Signup and view all the answers

What is the result of simplifying the expression $ rac{(ab)^2}{a^2b^4}$?

<p>$ rac{1}{b^2}$ (C)</p> Signup and view all the answers

Given the expression $a^3(a^{-1}b^2)$, what is the simplified result?

<p>$a^2b^2$ (C)</p> Signup and view all the answers

Which statement describes the common factor method of factorization for the expression $a^3 - a^2$?

<p>Factoring out $a^2$ yields $a^2(a - 1)$ (C)</p> Signup and view all the answers

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