Question

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

Answer 1

∑ Hey, jillianwagler ⊃

Answer:

$\frac{25a^4}{b^6c^8}$

Step-by-step 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: $(b^-^3)^2:\frac{1}{b^6}$

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

Simplify: $(c^{-4}\right))^2:\frac{1}{c^8}$

$=25a^4\frac{1}{b^6}\cdot \frac{1}{c^8}$

Simplify again:

$=\frac{25a^4}{b^6c^8}$

Finally Answer: $=\frac{25a^4}{b^6c^8}$

xcookiex12

8/19/2022