Exponent and Log Properties

(2m⁴)(5m²)

• 10m⁶

• 10m⁸

• 7m⁶

• 7m⁸

Answer explanation

To multiply two monomials, multiply the coefficients and add the exponents of the same variable. In this case, the coefficient is 2*5=10 and the variable is m. The exponents are 4+2=6. Therefore, the answer is 10m^6.

Tags

CCSS.8.EE.A.1

(6x²)(-3x⁵)

• 18x⁷

• -18x⁷

• 18x⁷

• 3x⁷

Answer explanation

To multiply two terms, multiply the coefficients and add the exponents of the variables. In this case, (-3) * (6) = -18 and (x^5) * (x^2) = x^7. Therefore, the correct answer is -18x^7.

Tags

CCSS.7.NS.A.2C

What is the value of (-2)^3?

• -8

• -6

• 6

• 8

Answer explanation

The value of (-2)³ is -8 because when a negative number is raised to an odd power, the result is negative. Therefore, the correct choice is -8.

Tags

CCSS.8.EE.A.1

1.)  Simplify
 (2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Answer explanation

To simplify the expression (2a^2b^4z)(6a^3b^2z^5), multiply the coefficients (2 * 6 = 12) and add the exponents for each variable (a^2 * a^3 = a^5, b^4 * b^2 = b^6, z * z^5 = z^6). The correct answer is 12a^5b^6z^6.

Tags

CCSS.HSA.APR.A.1

Which number is the BASE?
2³ = 8

• 2

• 3

• 8

Answer explanation

The base number is the number that is raised to a power. In this case, 2 is the base because it is raised to the power of 3, resulting in 8.

Tags

CCSS.6.EE.A.1

Evaluate the expression using the quotient of powers rule.

• a⁸b¹³

• a²b⁷

• a¹⁵b³⁰

• a⁸b⁷

Answer explanation

The quotient of powers rule states that when dividing two powers with the same base, subtract the exponents. In this case, a⁸b¹³ divided by a¹⁵b³⁰ simplifies to a^8-15b^13-30 which is equal to a^-7b^-17. Therefore, the correct choice is a²b⁷.

Tags

CCSS.8.EE.A.1

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Tags

CCSS.8.EE.A.1

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

Answer explanation

Logarithmic functions are the inverse of exponential functions.

Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

Answer explanation

To change log₆36 = 2 to exponential form, we use the property log_bx = y is equivalent to b^y = x. Therefore, 6² = 36 is the correct choice.

Tags

CCSS.HSF.BF.B.5

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

• add

• subtract

• multiply

• divide

Answer explanation

When you have two log expressions separated by a minus sign (-), you need to divide them to simplify into one log expression.