Surds and indices

Simplify
(45x⁶y²)/(5x⁴y⁹)

• (9x²)/y⁷
• 40x²y⁷
• 9x²y⁷
• 9x¹⁰y¹¹

Simplify
(16x⁴y^-5)/(8a³b^-8)

• (a³y⁵)/(2x⁴b⁸)
• (2x⁴b⁸)/(a³y⁵)
• (8x⁴b⁸)/(a³y⁵)
• 2x⁴b⁸a³y⁵

(ab⁸c)(a^-17c¹⁰)

• a¹⁷b⁸c¹¹
• a¹⁶b⁸c¹¹
• (b⁸c¹¹)/(a¹⁶)
• a^-17b⁸c¹⁰

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

If 5ⁿ = 125 find n.

• 25
• 1/3
• -3
• 3

Tags

CCSS.HSF.LE.A.4

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

Solve 16^{2x - 1} = 64

• 1.5
• 1.25
• 4/5
• -1.25

Tags

CCSS.HSF.LE.A.4

CCSS.HSF.BF.B.5

(ab⁸c)(a^-17c¹⁰)

• a¹⁷b⁸c¹¹
• a¹⁶b⁸c¹¹
• (b⁸c¹¹)/(a¹⁶)
• a^-17b⁸c¹⁰

Simplify (4pq³)² ÷ (2p²q)³.

• 2p⁻⁴q³

• 8p⁴q³

• 16p⁴q²

• 4p⁻⁴q²

Expand and simplify  $\left(\sqrt{2}+\sqrt{3}\right)^2$  

•  $2+5\sqrt{6}$  

•  $5+3\sqrt{2}$  

•  $5+2\sqrt{6}$  

•  $5+6\sqrt{2}$  

Rationalise  $\frac{\sqrt{2}+1}{\sqrt{2}-1}$  

•  $3-2\sqrt{2}$  

•  $2\sqrt{2}+6$  

•  $3+4\sqrt{6}$  

•  $3+2\sqrt{2}$  

Simplify  $27^{\frac{-1}{3}}$  

•  $\frac{1}{3}$  

•  $\frac{1}{27}$  

•  $-\frac{1}{3}$  

•  $\frac{27}{3}$