Which expression is equivalent to RootIndex 4 StartRoot 144 a Superscript 12 Baseline b cubed EndRoot? Assume a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0. 2 a cubed (RootIndex 4 StartRoot 9 b cubed EndRoot) 2 a Superscript 4 Baseline b (RootIndex 4 StartRoot 18 EndRoot) 6 a cubed (RootIndex 4 StartRoot 3 b cubed EndRoot) 12 a Superscript 6 Baseline b (RootIndex 4 StartRoot b EndRoot)

2 a^3 b ^3/4 * 3^1/2

2 a^3 b ^3/4  9^ 1/4

Step-by-step explanation:

(144 a^12 b^3) ^ (1/4)

Rewriting

12 ^2 ^1/4  a^12^1/4  b^3^1/4

We know a^b^c = a^ (b*c)

12 ^ 1/2  a^3 b^3/4

(4*3) ^ 1/2  a^3 b^3/4

We know (ab)^c = a^c * b^c

4^1/2   * 3^1/2

2 a^3 b ^3/4 * 3^1/2

Rewriting 3 as 9 ^ 1/4

2 a^3 b ^3/4  9^ 1/4

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: