7.1 Zero and Negative Exponents

Simplify

• 7a⁵/b³

• b³/7a⁵

• 7b³/a^-5

• 7b³ /a⁵

Answer explanation

To simplify, we recognize that the expression reduces to 7b³/a⁵. The other options either misplace the variables or do not simplify correctly. Thus, the correct answer is 7b³/a⁵.

Tags

CCSS.HSA.APR.A.1

Simplify

• -1/16

• 1/16

• -16

• 16

Answer explanation

To simplify, we can rewrite the expression and reduce it. The correct simplification leads to 1/16, which is the positive fraction among the choices. Thus, the answer is 1/16.

Tags

CCSS.8.EE.A.1

Simplify

• -1/125

• 125

• -125

• 1/125

Answer explanation

To simplify, recognize that 1/125 is equivalent to 125 raised to the power of -1. Thus, the correct answer is 1/125.

Tags

CCSS.8.EE.A.1

Simplify

• a³b²/4

• 4a³/b²

• 4/a³b²

• 1/4a³b²

Answer explanation

To simplify, we recognize that 4 can be expressed as 4/1. Thus, the expression simplifies to 4/(a^3 * b^2), which matches the correct answer choice 4/a^3b^2.

Tags

CCSS.HSA.APR.A.1

Simplify

• b³/64a⁵

• b³/16a⁵

• a⁵/64b³

• b³/-64a⁵

Answer explanation

To simplify, divide b^3 by 64a^5. The correct choice is b^3/64a^5, as it maintains the proper ratio of the variables and constants.

Tags

CCSS.8.EE.A.1

Rewrite using a positive exponent.
w^-13

• -w¹³

• ¹/_w¹³

• ¹/_w^-13

• w¹³

Answer explanation

To rewrite w^-13 using a positive exponent, apply the rule that a negative exponent indicates a reciprocal. Thus, w^-13 becomes 1/w^13, making the correct choice ¹/_w¹³.

Tags

CCSS.8.EE.A.1

Solve (-8)^-2

• 1/(-8)²

• 1/8²

• 1/64

• -64

Answer explanation

To solve (-8)^{-2}, use the property a^{-n} = 1/a^{n}. Thus, (-8)^{-2} = 1/(-8)^{2}. Calculating (-8)^{2} gives 64, so the final answer is 1/64.

Tags

CCSS.7.NS.A.2C

Anything raised to a power of zero is always: 

• 0

• 1

• itself

• negative

Answer explanation

Any number raised to the power of zero equals 1, except for zero itself. Therefore, the correct answer is 1.

Tags

CCSS.8.EE.A.1

Rewrite using a positive exponent.
g^-7

• ¹/_g⁷

• g⁷

• ¹/_g^-7

• -g⁷

Answer explanation

To rewrite g^-7 with a positive exponent, apply the rule that a negative exponent indicates the reciprocal. Thus, g^-7 becomes ¹/_g⁷, which is the correct choice.

Tags

CCSS.8.EE.A.1

Simplify

• -1/64

• 1/16

• 64/1

• 1/64

Answer explanation

To simplify, recognize that 1 divided by 64 equals 1/64. This matches the correct answer choice, which is 1/64.

Tags

CCSS.8.EE.A.1