PRACTICE #2 (Exponent Rules, Multiplying, Dividing, Power of a P

Answer explanation

To simplify -11a^4b^9 + 6a^4b^9, combine like terms: (-11 + 6)a^4b^9 = -5a^4b^9. The correct answer is -5a^4b^9.

Answer explanation

Combine like terms: -k - 8k = -9k and 5k^2 - 3k^2 = 2k^2. Thus, the simplified expression is 2k^2 - 9k, which matches the correct answer choice.

Directions: Simplify the following monomials. Express final answers using only positive exponents. Subtract 2m from (-7m).

• -9m

• -5m

• 5m

• 9m

Answer explanation

To simplify, subtract 2m from -7m: -7m - 2m = -9m. Thus, the correct answer is -9m.

Directions: Simplify the following monomials. Express final answers using only positive exponents. 4. Simplify x^8 * x^3.

• x^{11}

• x^5

• x^{24}

• x^9

Answer explanation

To simplify x^8 * x^3, use the property of exponents that states a^m * a^n = a^(m+n). Here, 8 + 3 = 11, so the simplified form is x^{11}. Therefore, the correct answer is x^{11}.

Tags

CCSS.8.EE.A.1

• -45 / k^7

• 45 / k^7

• -45k^7

• -45 / k^-7

Answer explanation

To simplify -15k^3 * 3k^{-10}, multiply the coefficients: -15 * 3 = -45. For the powers of k, add the exponents: 3 + (-10) = -7. Thus, the expression simplifies to -45 / k^7, which is the correct answer.

Tags

CCSS.HSA.APR.A.1

• 18s^14 / r^4

• 18r^4s^14

• -18s^14 / r^4

• -18r^4s^14

Answer explanation

To simplify (-9rs^2) * (-2r^{-5}s^{12}), multiply coefficients: 18. For r: r^1 * r^{-5} = r^{-4} (use positive exponent: 1/r^4). For s: s^2 * s^{12} = s^{14}. Final result: 18s^{14}/r^4.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify \( \frac{w^{12}}{w^{3}} \), use the property of exponents: \( a^m / a^n = a^{m-n} \). Thus, \( w^{12-3} = w^9 \). The correct answer is \( w^9 \).

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify \( \frac{40p^8q^2}{-5p^2q^3} \), divide the coefficients (40/-5 = -8) and subtract the exponents of like bases (\(p^{8-2} = p^6\) and \(q^{2-3} = q^{-1}\)). This gives \( \frac{-8p^6}{q} \), the correct answer.

• 2d^8 / 5c^3

• 2d^-8 / 5c^-3

• 5c^3 / 2d^8

• 5c^-3 / 2d^-8

Answer explanation

To simplify \( \frac{6c^{-1}d^{-3}}{15c^2d^{-11}} \), divide coefficients and subtract exponents: \( \frac{6}{15} = \frac{2}{5} \), \( c^{-1}/c^2 = c^{-3} \), and \( d^{-3}/d^{-11} = d^{8} \). Thus, the result is \( \frac{2d^8}{5c^3} \).

Tags

CCSS.HSA.APR.A.1

Answer explanation

To simplify (x^5)^6, use the power of a power property: multiply the exponents. Thus, 5 * 6 = 30, resulting in x^{30}. Therefore, the correct answer is x^{30}.

Tags

CCSS.8.EE.A.1