Exponents –multiplying monomials

Answer explanation

To simplify b^3 × b^4, use the property of exponents that states a^m × a^n = a^(m+n). Here, 3 + 4 = 7, so b^3 × b^4 = b^7. Thus, the correct answer is b^7.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify \(5^7 \times 5^3\), use the property of exponents: \(a^m \times a^n = a^{m+n}\). Thus, \(5^{7+3} = 5^{10}\). The simplified form is \(5^{10}\).

Tags

CCSS.8.EE.A.1

Answer explanation

Using the property of exponents, we combine the powers: (-2)^7 × (-2)^1 = (-2)^(7+1) = (-2)^8. Since (-2)^8 = 256, but the base is negative, the result is -256. Thus, the correct answer is (-2)^8 = -256.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify, use the property of exponents: a^m × a^n = a^(m+n). Here, (-2/3)^4 × (-2/3)^5 = (-2/3)^(4+5) = (-2/3)^9. Evaluating gives (-2)^9 = -512 and 3^9 = 19683, so the answer is (-2/3)^9 = -512/19683.

Tags

CCSS.8.EE.A.1

Answer explanation

To multiply the monomials, multiply the coefficients (4 * 3 = 12) and add the exponents of x (2 + 5 = 7). Thus, (4x^2)(3x^5) = 12x^7, which is the correct answer.

Tags

CCSS.8.EE.A.1

Answer explanation

To multiply the monomials, multiply the coefficients (3 and 5) to get 15, and add the exponents of x (6 and 2) to get x^8. Thus, (3x^6)(5x^2) = 15x^8, which is the correct answer.

Tags

CCSS.8.EE.A.1

• 20c^{10}

• 12c^21

Answer explanation

To multiply the monomials, multiply the coefficients (10 * 2 = 20) and add the exponents of c (7 + 3 = 10). Thus, (10c^7)(2c^3) = 20c^{10}. The correct answer is 20c^{10}.

Tags

CCSS.8.EE.A.1

• -15a^8b^5

Answer explanation

To multiply the monomials, multiply the coefficients (-3 and 5) to get -15. Then, add the exponents of like bases: a^(1+7) = a^8 and b^(4+1) = b^5. Thus, the result is -15a^8b^5.

Tags

CCSS.8.EE.A.1

• 34x^21

• 19x^21

Answer explanation

To simplify (2x^3)(17x^7), multiply the coefficients: 2 * 17 = 34. For the variables, add the exponents: 3 + 7 = 10. Thus, the expression simplifies to 34x^{10}, which is the correct answer.

Tags

CCSS.8.EE.A.1

• 18b^7

• 18b^10

Answer explanation

To simplify (3b^5)(6b^2), multiply the coefficients: 3 * 6 = 18. For the variables, add the exponents: 5 + 2 = 7. Thus, the expression simplifies to 18b^7, which is the correct answer.

Tags

CCSS.8.EE.A.1