Quiz 6.1 Review

Solve: x² = 64

• only -8

• only 8

• -8 AND 8

• 32

Answer explanation

x² = 64

Take the square root of both sides to get x = +8 OR x = -8.

Remember: 8 * 8 = 64, just like -8 * -8 = 64 :)

Tags

CCSS.8.EE.A.2

Assuming the value is nonzero, anything to the power of 0 is 1.

• TRUE :D

• FALSE >:[

Answer explanation

Assuming the value is nonzero, anything to the power of 0 is 1.

TRUE!

This is the Zero Exponent rule :D

Tags

CCSS.8.EE.A.1

Simplify the expression x⁸y² * x²y

• x¹⁰y²

• x¹⁰y³

• x¹⁶y²

• x¹⁶y³

Answer explanation

x⁸y² * x²y

x⁸ * x² = x¹⁰

y² * y = y³

Put it together to get x¹⁰y³

Simplify: (a³b²)⁴

• a¹²b⁸

• a⁷b⁶

• a¹²b⁶

• 4a³b²

Answer explanation

(a³b²)⁴

This is an example of the Power Rule, so we multiply the exponents.

(a³b²)⁴

a^3*4b^2*4

ANSWER: a¹²b⁸

Simplify: (x²y⁴) / (x⁵y)

• 1

• x³y³

• y³ / x³

• y⁴ / x³

Answer explanation

(x²y⁴) / (x⁵y)

First simplify x² / x⁵:

There's 3 more x's in the denominator, so it would become 1 / x³.

Then simplify y⁴ / y:

There's 3 more y's in the numerator, so it would become y³.

Put it all together to make it y³ / x³

Simplify: 1 / x^-2

• x²

• 1 / 2x

• 1 / x²

• -2x

Answer explanation

1 / x^-2 uses the negative exponent rule.

This means x^-2 must be moved to the numerator to make the exponent positive.

1 / x^-2 = x²

To rewrite x^-2y / 4 without negative exponents, it would become y / 4x²

• TRUE :D

• FALSE >:[

Answer explanation

To rewrite x^-2y / 4 without negative exponents, it would become y / 4x²

TRUE!

x^-2 is the only base that has a negative exponent.

When it is moved to the denominator, the exponent becomes positive. Everything else stays where it was :)

Simplify: 9h⁶ / 3h³

• 3h⁹

• 3h³

• 3h¹⁸

• h³

Answer explanation

9h⁶ / 3h³

Simplify 9 / 3 = 3

Simplify h⁶ / h³ = h³

Put it all together to get 3h³

Tags

CCSS.HSA.APR.A.1

Simplify: (x³ / y⁴) ⁵

• x³

• xy⁷

• x⁸ / y⁷

• x¹⁵ / y²⁰

Answer explanation

(x³ / y⁴) ⁵

Multiply the exponents inside of the parentheses with the outer exponent.

x^3*5 / y^4*5

ANSWER: x¹⁵ / y²⁰

Tags

CCSS.HSA.APR.A.1

Simplify: (4x²y³)⁰ / 8x³

• 1

• 1 / 8x³

• y³ / 2x

• 4y³ / 8x

Answer explanation

(4x²y³)⁰ / 8x³

(4x²y³)⁰ = 1 because of the Power Rule and Zero Exponent Rule.

This leaves 1 / 8x³, which cannot be simplified any more.

ANSWER: 1 / 8x³