Simplify the expression answer must be in positive exponents (5a^2b^-3c^-4)^2

Question

asked Feb 7, 2023 106k views

1 Answer

Beau Smith · Answer 1 · 2023-02-12T12:57:16+0000

∑ Hey, jillianwagler ⊃

Answer:

(25a^4)/(b^6c^8)

Explanation:

Given:

Simplify the expression answer must be in positive exponents

(5a^2b^-^3c^-^4)^2

Solve:

Applying exponent rules~:
$\left(a\cdot \:b\right)^n=a^nb^n$

Thus,

$\left(5a^2b^(-3)c^(-4)\right)^2=5^2\left(a^2\right)^2\left(b^(-3)\right)^2\left(c^(-4)\right)^2$

$=5^2\left(a^2\right)^2\left(b^(-3)\right)^2\left(c^(-4)\right)^2$

Simplify:
5^2=25

Now we have;

$=25\left(a^2\right)^2\left(b^(-3)\right)^2\left(c^(-4)\right)^2$

Simplify:
(a^2)^2:a^4

$=25a^4\left(b^(-3)\right)^2\left(c^(-4)\right)^2$

Simplify:
(b^-^3)^2:(1)/(b^6)

$=25a^4(1)/(b^6)\left(c^(-4)\right)^2$

Simplify:
$(c^(-4)\right))^2:(1)/(c^8)$

$=25a^4(1)/(b^6)\cdot (1)/(c^8)$

Simplify again:

=(25a^4)/(b^6c^8)

Finally Answer:
=(25a^4)/(b^6c^8)

xcookiex12

8/19/2022