Question

Which values of a and b make the equation true? (2xy)^4 ---------- =4x^a (y^b) 4xy

Answer 1

Answer:

B) a = 3, b = 3 .

Step-by-step explanation:

Given : $(2xy)^{4}$ = $4x^{a} (y^{b})4xy$.

To find : Which values of a and b make the equation true.

Solution : We have given that $(2xy)^{4}$ = $4x^{a} (y^{b})4xy$.

By exponential  same base rule :$x^{n} x^{m} = x^{m+n}$ if base are same then power will be add.

$2^{4} x^{4} y^{4}$ = $16x^{a+1} y^{b+1}$.

Solving exponent

16$x^{4} y^{4}$ =  $16x^{a+1} y^{b+1}$.

On equating x variable

$x^{4}$ =  $x^{a+1}$.

By exponent rule : if $x^{m}$ =  $x^{n}$ then m =n.

So, 4 = a+1

On subtracting by 1 both sides

a = 3.

On equating y variable ,

4 = b+1

On subtracting by 1 both sides

b = 3 .

Therefore, B) a = 3, b = 3 .

Answer 2

(2xy)^4=4x^a(y^b)4xy
16x^4y^4=16x^(a+1)y^(b+1)
4=a+1 4=b+1
3=a 3=b