Question

Simplify: 5^(2)x 5^(4)x5^(-4)x5^(-2)

Answer 1

Answer:

$320x^{15}$

Step-by-step explanation:

1. take out constants

( 5 × 2 × 4 × - 4 × - 2) $x^{5} x^{5} x^{5}$

2. simplify 5 × 2 to 10

(10 × 4 - 4 × - 2)$x^{5} x^{5} x^{5}$

3. simplify 10 × 4 to 40

(40 × - 4 × - 2)$x^{5} x^{5} x^{5}$

4. simplify 40 × -4 to -160

(-160 × - 2)$x^{5} x^{5} x^{5}$

5. simplify -160 × -2 to 320

$320x^{5} x^{5} x^{5}$

6. use product rule:$x^{a} x^{b} =x^{a+b}$

$320x^{5+5+5}$

7. simplify 5 + 5 to 10

$320x^{10+5}$

8. simplify 10 + 5 to 15 $320x^{15}$