Evaluate the expression.
a3b2c-1d
evaluate a2b2c1d
if a = 2, b = 4, c = 10, d = 15
express your answer
as a reduced fraction.

3/4 if meant

is

Step-by-step explanation:

So the expression we want to evaluate for

is

Please make sure I typed the expression and the values for the letters right.

Plug in the given values:

In the following step I said 2^3 equals 8 because 2^3 means 2*2*2.  I also got rid of the negative exponents by taking reciprocal.

In the following step I said 4^2=16 because 4^2 means 4*4.  I also wrote 10^1 as 10.

In the following step, I'm going to rewrite everything as a fraction if it isn't already a fraction.  8=8/1 and 15=15/1.

To multiply fractions, you just multiply straight across on top and straight across on bottom.

Actually performing the multiplication:

Time to reduce:

I divided top and bottom by 10 to get this.

One more time for reducing:

I divided top and bottom by 4 to get this.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

step-by-step explanation: